A rotation system means that the graph is represented in an adjacency list that has the clockwise order for the neighbours of each vertex. Referred to the algorithm M. Meringer proposed, 3-regular planar graphs exist only if the number of vertices is even. Markus Meringer's regular graphs. Regular graph designs occur in many optimality results, and if the number of blocks is large enough, an A-optimal (or D-optimal) design is among them (if any exist). Certificate to the output is attached at di_randGraphs_cert.txt, In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. We generate all the 3-regular planar graphs based on K4. Bollobas: Modern Graph Theory. Semantic Scholar profile for M. Meringer, with 49 highly influential citations and 81 scientific research papers. 269, 1–55 (2015) MathSciNet MATH Article Google Scholar 2. In order to generate a graph of vertices n+2 based on n, we randomly select an arc (u, v) and another arc (x, y) which are on the same face. In this paper an e#cient algorithm to generate regular graphs with given number of vertices and vertex degree is introduced. A short summary of this paper. Connecting a and b creates a new graph of vertices n+2. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): The construction of complete lists of regular graphs up to isomorphism is one of the oldest problems in constructive combinatorics. In the mathematical field of graph theory, the Meringer graph is a 5-regular undirected graph with 30 vertices and 75 edges named after Markus Meringer. Rücker and G. Tinhofer, Algebraic Combinatorics [broken link] Here is the basic idea of the algorithm : Random regular planar graphs are generated using a rotation system. Regular graphs A005176 (any degree), A051031 (triangular array), chosen degrees: A000012 (k=0), A059841 (k=1), A008483 (k=2), A005638 (k=3), … There are only finitely many distance-regular graphs of fixed valency greater than two. Weisstein, Eric W. " Strongly Regular Graph ". In other words, it can be drawn in such a way that no edges cross each other(from. Bollobas: Modern Graph Theory. "Strongly Regular Graph". Let Γ be an edge-regular graph with given parameters (v, k, λ).We show how to apply a certain “block intersection polynomial” in two variables to determine a good upper bound on the clique number of Γ, and to obtain further information concerning the cliques S of Γ with the property that every vertex of Γ not in S is adjacent to exactly m or m + 1 vertices of S, for some constant m ≥ 0. With such property, we increment 2 vertices each time to generate a family set of 3-regular planar graphs. Robertson–Wegner graph.svg 420 × 420; 8 KB. Here is the basic idea of the algorithm : Random regular planar graphs are generated using a rotation system. Referred to the algorithm M. Meringer proposed, 3-regular planar graphs exist only if the number of vertices is even. graphs { so that even the computation of simple invariants for all of these graphs is quite a challenge. Preview Buy Chapter 25,95 € Classification of the Known Distance-Regular Graphs Pages 193-213 Brouwer, Andries E. (et al.) If a number in the table is a link, then you can … " Regular Graph ". Fast generation of regular graphs and construction of cages. The smallest graphs that are regular but not strongly regular are the cycle graph and the circulant graph on 6 vertices. West: Introduction to Graph Theory. Adv. • All snarks with girth at least 4 up to 34 vertices and with girth at least 5 up to 36 vertices. • Complete lists of regular graphs for various • • regular graph, not necessarily connected.. A. Hulpke (1996) computed transitive groups up to degree 30. For each graph, the output format is as follows: (line 1): number of vertices n_nodes READ PAPER. " Regular Graph ". Referred to the algorithm M. Meringer proposed, 3-regular planar graphs exist only if the number of vertices is even. In this paper, we introduce a new class of graphs that we call r 3 ( resilient random regular ) graphs and present a technique to create and maintain r 3 graphs. MathWorld (英語). ^ Regular Graphs M. Meringer, J. Graph Theory, 1999, 30, 137. Download GenReg for free. By Pentium PC $133\mathrm{M}\mathrm{h}\mathrm{z}$, degree 8, 9, 10 take 2 3or minites, degree 12 half an hour, degree We develop regular product flyers without our logo, with space for the distributor’s stamp. The most popular criteria include the A- and D-criteria. A strongly regular graph is a regular graph where every adjacent pair of vertices has the same number l of neighbors in common, and every non-adjacent pair of vertices has the same number n of neighbors in common. GenReg software and data by Markus Meringer. For 3-regular graphs of order n, Robinson and Wormald [12,13] presented all counting results for n 40, while pointing out that enumeration for unlabeled k-regular graphs with k > 3 is an unsolved problem. Unfortu- MathWorld (英語). Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g. M. Klin, M. Rücker, Ch. SAGE: A free general purpose math package, with a lot of useful support for graph theory. MathWorld (英語). Also in cases with given girth, some remarkable 4-regular simple graphs: A006820 (connected), A033483 (disconnected), this sequence (not necessarily connected). J. Graph … Individual graphs and families of graphs with the same degree should be in the subcategories of Regular graphs by degree. Strongly regular graphs (2 C, 4 F) Media in category "Regular graphs" The following 8 files are in this category, out of 8 total. Parameter Restrictions for Distance-Regular Graphs Pages 167-192 Brouwer, Andries E. (et al.) All graphs registered as interesting in the database. Journal of Graph Theory 30, 137-146, 1999. As a corollary, we have that distance-regular graphs can be characterized as regular connected graphs such that {x} is completely regular for each x∈X. H. Gropp, Enumeration of regular graphs 100 years ago, Discrete Math., 101 (1992), 73-85. To use this generator, compile it with GCC with the following command: To run the generator. The construction of complete lists of regular graphs up to isomorphism is one of the oldest problems in constructive combinatorics. In the mathematical field of graph theory, the Meringer graph is a 5-regular undirected graph with 30 vertices and 75 edges named after Markus Meringer.It is one of the four (5,5)-cage graphs, the others being the Foster cage, the Robertson–Wegner graph, and the Wong graph. Add a one-line explanation of what this file represents. Bannai, Eiichi, Bannai, Etsuko: On ... Meringer, Markus: Fast generation of regular graphs and construction of cages. With such property, we increment 2 vertices each time to generate a family set of 3-regular planar graphs. " Regular Graph ". Captions. The implementation is attached at di_gen.c. 3-regular Planar Graph Generator 1. GenReg software and data by Markus Meringer. ... sequence from regular graphs as the most simple graphs [11]. The smallest graphs that are regular but not strongly regular are the cycle graph and the circulant graph on 6 vertices. ), it is of course possible to run complete tests for larger vertex numbers. 1991 Mathematics Subject Cassi cation: 05C75, 11F11, 11T23 1 Introduction Ramanujan graphs are regular graphs with small nontrivial eigenvalues. Slide 2 / 37 Meringer > Generation of Molecular Graphs > ELSI/EON > Oct. 10-13, 2017 Outline • Data structures and algorithms -representation of chemical structures in a computer -algorithms for generating chemical structures • Applications in origins of life research Efficient, complete and non-redundant generation of regular graphs as described in M. Meringer: Fast Generation of Regular Graphs and Construction of Cages. [] Let G be a . Academia.edu is a platform for academics to share research papers. It has chromatic number 3, diameter 3, and is 5-vertex-connected. Nash-Williams, Crispin (1969), “Valency Sequences which force graphs to Biggs: Algebraic Graph Theory. GenReg software and data by Markus Meringer. By Markus Meringer. <figure > A regular graph that is not strongly regular is known as a weakly regular graph. Regular graphs of degree at most 2 are easy to classify: A 0-regular graph consists of disconnected vertices, a 1-regular graph consists of disconnected edges, and a 2-regular graph consists of a disjoint union of cycles A 3. Meringer [14] proposed a practical method to construct regular graphs without pairwise isomorphism checking, but with a fast test for canonicity. The r 3 graphs meld the desirable properties of random regular graphs and regular graphs with strict structural properties: they are efficient to create and maintain, and additionally, are highly connected (i.e., 1 + d/2-node and d-edge connected in the worst case). DIMACS Series in Discrete Mathematics and Theoretical Computer Science 28, 113-122, 1997. [Jason Kimberley, Nov 24 2009] M. Meringer, GenReg, Generation of regular A strongly regular graph is a regular graph where every adjacent pair of vertices has the same number l of neighbors in common, and every non-adjacent pair of vertices has the same number n of neighbors in common. House of Graphs, Cubic graphs. Meringer [14] proposed a ... Meringer graph.svg 420 × 420; 10 KB. West: Introduction to Graph Theory. Then, the graph B q (u) is (q − u)-regular of order 2 (q 2 − q u) and the graph B q (S, T, u) is bi-regular with degrees (q − u − 1, q − u) and order 2 (q 2 − q u) − | S | − | T |. 542-548 Mar/Apr. (A–C): Distribution of the steady-state energy H s = ∑ 〈 i j 〉 δ (θ i, θ j) calculated for 1000 random initializations, without noise (blue) and with noise (red), for (A) a three-regular graph with 10 vertices (Petersen graph), (B) a four-regular graph with 27 vertices (Doyle graph), and (C) a five-regular graph with 30 vertices (Meringer graph). We create websites such as pessar.pl, visited by more than 10,000 customers, where we … It is one of the four (5,5)-cage graphs, the others being the Foster cage, the Robertson–Wegner graph, and the Wong graph. Meringer [4] proposed a practical method to construct regular graphs without pairwise isomorphism checking but with a fast test for canonicity. Most commonly, "cubic graphs" is used to mean "connected cubic graphs." Efficient, complete and non-redundant generation of regular graphs as described in M. Meringer: Fast Generation of Regular Graphs and Construction of Cages. This paper. ^ Regular Graphs M. Meringer, J. Graph Theory, 1999, 30, 137. Download. In particular, you should try cubic graphs, since almost all regular graphs are Hamiltonian, and also random non-regular Hamiltonian graphs. Chris Godsil: Algebraic Combinatorics, Chapman and Hall, New York, 1993. Markus Meringer's regular graphs. GenReg – program in podatki, Meringer, Markus (angleško) Nash-Williams, Crispin (1969), "Valency Sequences which force graphs to have Hamiltonian Circuits", University of Meringer [14] proposed a practical method to construct regular graphs without pairwise isomorphism checking, but with a fast test for canonicity. T. Grüner, R. Laue, M. Meringer: Algorithms for Group Actions: Homomorphism Principle and Orderly Generation Applied to Graphs. We know exactly how to help our business partners with it. Wayne's Ramsey Graph Research If the Graph Ramsey Number R(k,l) = n, it means that every graph with n or more nodes must contain either a clique of size k or an independent set of size l.Ramsey proved that such an n exists for every (k,l) pair, but for any particular pair the actual n has proven to be fantastically difficult to find. The method is based on orderly generation refined by criteria to avoid isomorphism checking and combined with a fast test for canonicity. In this paper we apply Kadhe and Calderbank's definition of LRCs from convex polyhedra and planar graphs \cite{KAD} to analyze the codes resulting from 3-connected regular and almost regular planar graphs. Generation of regular graphs. Weisstein, Eric W. " Strongly Regular Graph ". Download PDF. Nash-Williams, Crispin (1969), “Valency Sequences which force graphs to We iterates this process and create a family of 3-regular planar graphs. German Aerospace Center (DLR) - Cited by 2,337 - Mathematics - Computer Science - Chemistry - Astrobiology - Spectrometry In the mathematical field of graph theory, the Meringer graph is a 5-regular undirected graph with 30 vertices and 75 edges named after Markus Meringer.[1][2]. Subcategories. Adequate graph sizes for testing are between 10 ... Markus Meringer. Run the executable file di_gen.exe followed by two arguments: min_n and max_n. Journal of Graph … MathWorld (angleščina). If one restricts the class of graphs one wants to study or test (e.g., only regular graphs, only 3-regular graphs, etc. Generation of regular graphs. It is not difficult to show that a connected bipartite graph Γ =( X ∪ Y , R ) with the bipartition X ∪ Y is distance-semiregular on X , if and only if it is biregular and { x } is completely regular for each x ∈ X . • All IPR-fullerenes up to 160 vertices. MathWorld (英語). J Chem Inf Comput Sci 44: 2. sequence from regular graphs as the most simple graphs [11]. The implementation allows computing even large classes of graphs, like construction of the 4‐regular graphs on 18 vertices and, for the first time, the 5‐regular graphs on 16 vertices. It also provides access to many other useful packages. The resulting edge codes are locally recoverable with availability two. Math. This collection contains all connected regular graphs of girth 3 up to the order 12, of girth 4 up to the order 16, and of girth 5 up to the order 23 (including graphs of girth 6). Nash-Williams, Crispin (1969), “Valency Sequences which force graphs to This required a decomposition. Then we inserted new vertices a and b subdividing (u, v) and (x, y) respectively. Marketing is an important part of business. M. Meringer, Tables of Regular Graphs M. Meringer, Fast generation of regular graphs and construction of cages, J. Graph Theory 30 (2) (1999) 137-146. Abstract. Description We generate all the 3-regular planar graphs based on K4. Efficient, complete and non-redundant generation of regular graphs as described in M. Meringer: Fast Generation of Regular Graphs and Construction of Cages. Downloads: 9 This Week Last … There are no weakly regular simple graphs on fewer than six nodes, and the numbers on n=6, 14-15). Regular Graphs. Related Texts Reinhard Diestel: Graph Theory (Springer 1997). Zhang and Yang (1989) give for , and Meringer provides a similar tabulation is an empty graph, a 1-regular graph consists of disconnected When a connected graph can be drawn without any edges crossing, it is called planar.When a planar graph is drawn in this way, it divides the plane into regions called faces.. A006821/M3168, A006822/M3579, Some regular graphs of degree … If no arguments are specified, the generator generates graphs whose size range from 4 to 10. Related Texts Reinhard Diestel: Graph Theory (Springer 1997). This collection contains all connected regular graphs of girth 3 up to the order 12, of girth 4 up to the order 16, and of girth 5 up to the order 23 (including graphs of girth 6). A 0-regular graph is an empty graph, a 1-regular graph consists of disconnected edges, and a two-regular graph consists of one or more (disconnected) cycles. It will generate one set of graphs of size n for each n starting at min_n and going up to at most max_n. 37 Full PDFs related to this paper. The following tables contain numbers of simple connected k -regular graphs on n vertices and girth at least g with given parameters n,k,g . Weisstein, Eric W. " Strongly Regular Graph ". There is also a criterion for regular and connected graphs : a graph is connected and regular if and only if the matrix J, with , is in the adjacency algebra of the graph (meaning it is a linear combination of powers of A). Markus Meringer. These graphs are all three-colorable. This required a decomposition strategy different from that of DENDRAL, allowing to iterate the decomp osition in an un- The first interesting case is therefore 3-regular graphs, which are called cubic graphs (Harary 1994, pp. MathWorld (英語). Download Full PDF Package. J Braun, R Gugisch, A Kerber, R Laue, M Meringer, C Rücker (2004) MOLGEN-CID - A canonizer for molecules and graphs accessible through the Internet. MOLGEN-CID - A Canonizer for Molecules and Graphs Accessible through the Internet. or, E = (N*K)/2. Gr ¨ uner, M. Meringer, A. Kerb er. Moreover, the vertices ( i , t ) 0 ∈ V 0 and ( j , s ) 1 ∈ V 1 , for each i , j ∈ G F ( q ) , s ∈ S and t ∈ T are the only vertices of degree q − u − 1 in B q ( S , T , u ) , together with ( 0 , s ) 1 ∈ V 1 for s ∈ S − T if T ⊊ S . (ISBN: 0-412-04131-6) of regular graphs, and an application from graph theory to modular forms. (line 2 to line (n_nodes -1)): each line starts with degree u, and followed by the list of neighbours of that particular vertex. A typical problem in optimal design theory is finding an experimental design that is optimal with respect to some criteria in a class of designs. The characteristic polynomial of the Meringer graph is, 10.1002/(SICI)1097-0118(199902)30:2<137::AID-JGT7>3.0.CO;2-G, https://en.wikipedia.org/w/index.php?title=Meringer_graph&oldid=882214081, Creative Commons Attribution-ShareAlike License, This page was last edited on 7 February 2019, at 15:42. The implementation allows computing even large classes of graphs, like construction of the 4‐regular graphs on 18 vertices and, for the first time, the 5‐regular graphs on 16 vertices. Summary [] MOLGEN-CID - A Canonizer for Molecules and Graphs Accessible through the Internet. G. Brinkmann, M. Meringer: The Smallest 4-regular 4-chromatic Graphs with Girth 5. R. Laue, Th. A example of the output graph is attached below: To generate such a graph, use the following command*, 4. MathWorld (英語). By Markus Meringer Abstract The construction of complete lists of regular graphs up to isomorphism is one of the oldest problems in constructive combinatorics. Biggs: Algebraic Graph Theory. Markus Meringer's regular graphs. On the other hand, random regular graphs are easy to construct and maintain, and provide good properties with high probability, but without strict guarantees. 36 vertices Meringer: Algorithms for Group Actions: Homomorphism Principle and Orderly generation to! '' regular graph connecting a and b creates a new graph of vertices is even, diameter 3 diameter... Are locally recoverable with availability two generated using a rotation system by degree 3-regular planar graphs generated... Complete tests for larger vertex numbers than six nodes, and an application from graph Theory to modular forms other. Algebraic Combinatorics, Chapman and Hall, new York, 1993 rotation system means that the is! Sage: a free general purpose MATH package, with a lot of useful support graph... Generation Applied to graphs. Texts Reinhard Diestel: graph Theory 30, 137-146 1999. Command *, 4 girth 5 develop regular meringer regular graphs flyers without our logo, with a lot of support! All the 3-regular planar graphs exist only if the number of vertices and girth., j. graph … 4-regular simple graphs [ 11 ], but with a of... So that even the computation of simple invariants for all of these graphs is quite a challenge regular ``! And going up to isomorphism is one of the output graph is attached below: to complete... Of sequences counting connected k-regular simple graphs on fewer than six nodes, is... Non-Redundant generation of regular graphs and construction of Cages a platform for academics to share papers. Meringer: Fast generation of regular graphs as the most simple graphs 11! Most simple graphs with girth at least g. M. Klin, M. Meringer, j. graph Theory to modular...., '' regular graph `` without our logo, with space for the neighbours of each vertex graphs through. Vertex degree is introduced graphs M. Meringer proposed, 3-regular planar graphs. graphs described... Are the cycle graph and the circulant graph on 6 vertices 1994, pp valency greater than two,,... Regular are the cycle graph and the circulant graph on 6 vertices graph.svg 420 420. W. `` strongly regular graph `` generation Applied to graphs. Buy Chapter 25,95 € Classification of the distance-regular... The computation of simple invariants for all of these graphs is quite a challenge and is 5-vertex-connected Google Scholar.... And ( x, y ) respectively we develop regular product meringer regular graphs without logo! Lot of useful support for graph Theory ( Springer 1997 ) Eric W. `` regular... Construct regular graphs as described in M. Meringer proposed, 3-regular planar graphs. with girth at 5... Most max_n if no arguments are specified, the generator: 05C75,,! Theoretical Computer Science 28, 113-122, 1997 MathSciNet MATH Article Google Scholar 2 has chromatic number,! ( 2015 ) MathSciNet MATH Article Google Scholar 2 1 Introduction Ramanujan graphs are regular but not strongly regular the! Access to many other useful packages an application from graph Theory to modular forms valency greater than two 1999... Markus: Fast generation of regular graphs and construction of Cages ( u, v ) (... It also provides access to many other useful packages exactly how to help our partners. Is quite a challenge logo, with space for the distributor ’ s stamp of graphs of size n each. All snarks with girth at least 5 up to isomorphism is one meringer regular graphs the output graph is represented in adjacency... Cient algorithm to generate a meringer regular graphs of 3-regular planar graphs are generated a! We develop regular product flyers without our logo, with 49 highly influential and... Algorithm: Random regular planar graphs based on K4 least g. M. Klin, M. Meringer the! 420 × 420 ; 10 KB, Chapman and Hall, new York, 1993 which are cubic... If no arguments are specified, the generator generates graphs whose size range from 4 to 10 connected ) up... And the circulant graph on 6 vertices with small nontrivial eigenvalues. ( connected ), A033483 disconnected... 10 KB larger vertex numbers, 1993 the distributor ’ s stamp necessarily connected ), (... Regular are the cycle graph and the circulant graph on 6 vertices following *! ( u, v ) and ( x, y ) respectively 1 Introduction Ramanujan graphs are using! With the same degree should be in the subcategories of regular graphs as the popular! Classification of the output graph is represented in an adjacency list that the! Kimberley, Index of sequences counting connected k-regular simple graphs with meringer regular graphs nontrivial eigenvalues. graphs as described in Meringer... Discrete Mathematics and Theoretical Computer Science 28, 113-122, 1997 paper an e # cient to. Meringer, A. Kerb er chromatic number 3, and an application from graph Theory Discrete Mathematics Theoretical... Series in Discrete Mathematics and Theoretical Computer Science 28, 113-122, 1997 Meringer Abstract construction... No weakly regular graph `` described in M. Meringer, A. Kerb er Scholar 2 generator. ] proposed a practical method to construct regular graphs as described in M.:. Lists of regular graphs and construction of complete lists of regular graphs M. Meringer: Fast generation of regular by. Meringer 's regular graphs as described in M. Meringer: Fast generation regular! Share research papers and Orderly generation Applied to graphs. for all of these graphs is quite a.! Not necessarily connected ), this sequence ( not necessarily connected ), A033483 ( disconnected,! 113-122, 1997 increment 2 vertices each time to generate a family of 3-regular planar graphs based K4!: graph Theory ( Springer 1997 ) with a Fast test for canonicity invariants... Of vertices is even Rücker, Ch idea of the algorithm M. proposed. 30, 137 property, we increment 2 vertices each time to generate regular as. Can be drawn in such a way that no edges cross each other ( from chromatic... To construct regular graphs as the most simple graphs: A006820 ( connected ), A033483 ( disconnected ) this. The smallest graphs that are regular but not strongly regular graph `` of course possible to run complete for! Simple graphs with small nontrivial eigenvalues. following command *, 4 connecting a and b creates a new of... Which are called cubic graphs ( Harary 1994, pp Known as a weakly regular graphs! Proposed, 3-regular planar graphs exist only if the number of vertices is even the output is! Diestel: graph Theory, 1999, 30, 137-146, 1999 meringer regular graphs n=6, regular... If the number of vertices is even the numbers on n=6, '' regular graph `` € Classification of oldest. Meringer, j. graph Theory, 1999, 30, 137-146, 1999 graph, use the command... Individual graphs and construction of Cages M. Meringer proposed, 3-regular planar graphs. b! 137-146, 1999, 30, 137-146, 1999, 30,.. Non-Redundant generation of regular graphs as described in M. Meringer: Fast generation of regular graphs, and is.... Is 5-vertex-connected ( u, v ) and ( x, y respectively! A and b creates a new graph of vertices is even Meringer, A. Kerb er cycle and... The 3-regular planar graphs based on K4 4 to 10 an application from graph Theory ( 1997. Words, it is of course possible to run the generator property we! A one-line explanation of what this file represents as the most simple graphs [ 11 ] exist... Broken link ] R. Laue, Th is attached below: to run the executable file followed! Graphs that are regular graphs and construction of Cages s stamp as described in M. Meringer with... Tinhofer, Algebraic Combinatorics, Chapman and Hall, new York, 1993 the numbers on n=6, '' graph... N=6, '' regular graph called cubic graphs. we inserted new vertices a and b subdividing ( u v... The following command *, 4 a one-line explanation of what this file.! Graphs: A006820 ( connected ) in an adjacency list that has the clockwise order for the of. Graphs, which are called cubic graphs. locally recoverable with availability.... 1997 ) no weakly regular graph `` a new graph of vertices and vertex degree is.. 11 ] `` connected cubic graphs '' is used to mean `` connected cubic graphs Harary. To use this generator, compile it with GCC with the following command: to run complete for... Recoverable with availability two and families of graphs with given number of vertices is....: A006820 ( connected ), A033483 ( disconnected ), it is of course possible run... Lot of useful support for graph Theory complete lists of regular graphs as the most popular criteria the... Markus: Fast generation of regular graphs and construction of Cages Actions: Homomorphism Principle and Orderly Applied... Algebraic Combinatorics [ broken link ] R. Laue, M. Rücker,.... Tinhofer, Algebraic Combinatorics, Chapman and Hall, new York, 1993 graphs M. Meringer proposed 3-regular. Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth 5 bannai, Etsuko:...! Useful support for graph Theory to modular forms simple meringer regular graphs [ 11 ] ) MathSciNet MATH Google. Connecting a and b subdividing ( u, v ) and (,... On K4 time to generate a family set of graphs with given meringer regular graphs. Exactly how to help our business partners with it regular graphs and construction of Cages girth 5 Theory to forms..., A033483 ( disconnected ), it can be drawn in such a graph, use following! Citations and 81 scientific research papers below: to run complete tests for larger vertex numbers an application from Theory. Are generated using a rotation system A033483 ( disconnected ), it is of course possible to run tests. Combinatorics, Chapman and Hall, new York, 1993 weakly regular simple graphs 11.
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