# meringer regular graphs

Uncategorized

(line 2 to line (n_nodes -1)): each line starts with degree u, and followed by the list of neighbours of that particular vertex. Meringer  proposed a practical method to construct regular graphs without pairwise isomorphism checking but with a fast test for canonicity. 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 … Add a one-line explanation of what this file represents. Regular Graphs. GenReg software and data by Markus Meringer. " Regular Graph ". Rücker and G. Tinhofer, Algebraic Combinatorics [broken link] ... sequence from regular graphs as the most simple graphs . 3-regular Planar Graph Generator 1. Download Full PDF Package. 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 iterates this process and create a family of 3-regular planar graphs. MathWorld (英語). MathWorld (英語). GenReg software and data by Markus Meringer. <figure > A regular graph that is not strongly regular is known as a weakly regular graph. GenReg software and data by Markus Meringer. 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. Efficient, complete and non-redundant generation of regular graphs as described in M. Meringer: Fast Generation of Regular Graphs and Construction of Cages. The resulting edge codes are locally recoverable with availability two. or, E = (N*K)/2. 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. 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). 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. MathWorld (英語). (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). This required a decomposition strategy diﬀerent from that of DENDRAL, allowing to iterate the decomp osition in an un- In this paper an e#cient algorithm to generate regular graphs with given number of vertices and vertex degree is introduced. Weisstein, Eric W. " Strongly Regular Graph ". In other words, it can be drawn in such a way that no edges cross each other(from. Weisstein, Eric W. " Strongly Regular Graph ". 269, 1–55 (2015) MathSciNet MATH Article Google Scholar 2. Meringer  proposed a practical method to construct regular graphs without pairwise isomorphism checking, but with a fast test for canonicity. J. Graph … • Complete lists of regular graphs for various • • G. Brinkmann, M. Meringer: The Smallest 4-regular 4-chromatic Graphs with Girth 5. Adv. 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). By Markus Meringer Abstract The construction of complete lists of regular graphs up to isomorphism is one of the oldest problems in constructive combinatorics. MathWorld (英語). Abstract. A rotation system means that the graph is represented in an adjacency list that has the clockwise order for the neighbours of each vertex. Gr ¨ uner, M. Meringer, A. Kerb er. Strongly regular graphs (2 C, 4 F) Media in category "Regular graphs" The following 8 files are in this category, out of 8 total. The most popular criteria include the A- and D-criteria. We create websites such as pessar.pl, visited by more than 10,000 customers, where we … ^ Regular Graphs M. Meringer, J. Graph Theory, 1999, 30, 137. Marketing is an important part of business. Journal of Graph Theory 30, 137-146, 1999. The first interesting case is therefore 3-regular graphs, which are called cubic graphs (Harary 1994, pp. 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 . Most commonly, "cubic graphs" is used to mean "connected cubic graphs." West: Introduction to Graph Theory. Markus Meringer. Individual graphs and families of graphs with the same degree should be in the subcategories of Regular graphs by degree. If a number in the table is a link, then you can … 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). 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. Summary [] H. Gropp, Enumeration of regular graphs 100 years ago, Discrete Math., 101 (1992), 73-85. 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 . 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. "Strongly Regular Graph". We know exactly how to help our business partners with it. There are no weakly regular simple graphs on fewer than six nodes, and the numbers on n=6, 14-15). Regular graphs A005176 (any degree), A051031 (triangular array), chosen degrees: A000012 (k=0), A059841 (k=1), A008483 (k=2), A005638 (k=3), … Markus Meringer's regular graphs. 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.. Referred to the algorithm M. Meringer proposed, 3-regular planar graphs exist only if the number of vertices is even. West: Introduction to Graph Theory. 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 It has chromatic number 3, diameter 3, and is 5-vertex-connected. Connecting a and b creates a new graph of vertices n+2. Efficient, complete and non-redundant generation of regular graphs as described in M. Meringer: Fast Generation of Regular Graphs and Construction of Cages. 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. On the other hand, random regular graphs are easy to construct and maintain, and provide good properties with high probability, but without strict guarantees. Generation of regular graphs. Robertson–Wegner graph.svg 420 × 420; 8 KB. DIMACS Series in Discrete Mathematics and Theoretical Computer Science 28, 113-122, 1997. Biggs: Algebraic Graph Theory. 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. J Chem Inf Comput Sci 44: 2. 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. Referred to the algorithm M. Meringer proposed, 3-regular planar graphs exist only if the number of vertices is even. Math. 4-regular simple graphs: A006820 (connected), A033483 (disconnected), this sequence (not necessarily connected). By Pentium PC $133\mathrm{M}\mathrm{h}\mathrm{z}$, degree 8, 9, 10 take 2 3or minites, degree 12 half an hour, degree Downloads: 9 This Week Last … Bollobas: Modern Graph Theory. ^ Regular Graphs M. Meringer, J. Graph Theory, 1999, 30, 137. Markus Meringer's regular graphs. In particular, you should try cubic graphs, since almost all regular graphs are Hamiltonian, and also random non-regular Hamiltonian graphs. ‪German Aerospace Center (DLR)‬ - ‪Cited by 2,337‬ - ‪Mathematics‬ - ‪Computer Science‬ - ‪Chemistry‬ - ‪Astrobiology‬ - ‪Spectrometry‬ 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. If no arguments are specified, the generator generates graphs whose size range from 4 to 10. These graphs are all three-colorable. Markus Meringer's regular graphs. 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. We develop regular product flyers without our logo, with space for the distributor’s stamp. SAGE: A free general purpose math package, with a lot of useful support for graph theory. • All snarks with girth at least 4 up to 34 vertices and with girth at least 5 up to 36 vertices. 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 |. Also in cases with given girth, some remarkable (ISBN: 0-412-04131-6) The construction of complete lists of regular graphs up to isomorphism is one of the oldest problems in constructive combinatorics. If one restricts the class of graphs one wants to study or test (e.g., only regular graphs, only 3-regular graphs, etc. The method is based on orderly generation refined by criteria to avoid isomorphism checking and combined with a fast test for canonicity. MathWorld (angleščina). Semantic Scholar profile for M. Meringer, with 49 highly influential citations and 81 scientific research papers. Unfortu- Meringer  proposed a practical method to construct regular graphs without pairwise isomorphism checking, but with a fast test for canonicity. 37 Full PDFs related to this paper. [Jason Kimberley, Nov 24 2009] M. Meringer, GenReg, Generation of regular MathWorld (英語). Weisstein, Eric W. " Strongly Regular Graph ". MOLGEN-CID - A Canonizer for Molecules and Graphs Accessible through the Internet. Biggs: Algebraic Graph Theory. 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. This paper. With such property, we increment 2 vertices each time to generate a family set of 3-regular planar graphs. Here is the basic idea of the algorithm : Random regular planar graphs are generated using a rotation system. Journal of Graph … Subcategories. By Markus Meringer. 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. 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). It is one of the four (5,5)-cage graphs, the others being the Foster cage, the Robertson–Wegner graph, and the Wong graph.  cubic graphs '' is used to mean  connected cubic graphs. for testing between... Using a rotation system the oldest problems in constructive Combinatorics '' is used mean... Called cubic graphs. means that the graph is represented in an adjacency list that the. Graphs based on K4 followed by two arguments: min_n and max_n iterates this process and create a family of! For graph Theory 30, 137-146, 1999 molgen-cid - meringer regular graphs Canonizer for Molecules and graphs through. Other useful packages is not strongly regular graph  10 KB Known a... Commonly,  cubic graphs '' is used to mean  connected cubic graphs '' is used mean..., and the circulant graph on 6 vertices new vertices a and b subdividing u... Semantic Scholar profile for M. Meringer proposed, 3-regular planar graphs are regular but not strongly regular ! Known distance-regular graphs of fixed valency greater than two Introduction Ramanujan graphs are regular graphs as described in M.:. By Markus Meringer number 3, diameter 3, diameter 3, diameter 3, diameter 3, diameter,. '' regular graph  of vertices is even: to run the generator generates graphs size... Are regular but not strongly regular graph  same degree should be in the of. To modular forms u, v ) and ( x, y ) respectively and non-redundant generation of graphs. An adjacency list that has the clockwise order for the distributor ’ s stamp and an application from graph,! Uner, M. Meringer: Fast generation of regular graphs as described in M. Meringer, A. er! Arguments are specified, the generator generates graphs whose size range from 4 10! Theory ( Springer 1997 ), j. graph Theory 30, 137-146, 1999 Group... Connected ): a free general purpose MATH package, with 49 highly influential citations and scientific... Kimberley, Index of sequences counting connected k-regular simple graphs [ 11.. Arguments are specified, the generator generates graphs whose size range from 4 to 10 Meringer,., 1–55 ( 2015 ) MathSciNet MATH Article Google Scholar 2 y ) respectively vertices n+2 property! B creates a new graph of vertices is even circulant graph on 6 vertices with a Fast test canonicity... [ ] Semantic Scholar profile for M. Meringer: the smallest graphs that are regular graphs as the most graphs. Mathematics Subject Cassi cation: 05C75, 11F11, 11T23 1 Introduction graphs... Two arguments: min_n and max_n 1–55 ( 2015 ) MathSciNet MATH Article Google Scholar 2 is of possible. ( Springer 1997 ) 1–55 ( 2015 ) MathSciNet MATH Article Google Scholar 2 4-chromatic graphs with girth at 4. Molecules and graphs Accessible through the Internet up to at most max_n,.! For testing are between 10... Markus Meringer here is the basic idea of algorithm... Many distance-regular graphs Pages 193-213 Brouwer, Andries E. ( et al. non-redundant. Least 5 up to at most max_n criteria include the A- and D-criteria platform for to... To isomorphism is one of the Known distance-regular graphs Pages 193-213 Brouwer, Andries E. ( et al. the... A practical method to construct regular graphs up to 36 vertices A. Kerb er to construct regular graphs construction. Then we inserted new vertices a and b subdividing ( u, v ) and ( x, )! Graphs ( Harary 1994, pp [ ] Semantic Scholar profile for M. Meringer: Fast generation regular., but with a lot of useful support for graph Theory 30, 137 the oldest problems in Combinatorics. For academics to share research papers  strongly regular are the cycle graph and the graph... Are generated using a rotation system Eiichi, bannai, Eiichi, bannai, Eiichi, bannai, Eiichi bannai... With it M. Rücker, Ch: min_n and going up to vertices... { so that even the computation of simple invariants for all of graphs. Words, it is of course possible to run complete tests for larger vertex numbers for! Meringer: Algorithms for Group Actions: Homomorphism Principle and Orderly generation Applied to graphs. each to! Theoretical Computer Science 28, 113-122, 1997 Algebraic Combinatorics [ broken ]. Graph on 6 vertices Ramanujan graphs are generated using a rotation system and the circulant graph on vertices... 11 ] most max_n each n starting at min_n and going up to isomorphism is one of algorithm., but with a lot of useful support for graph Theory ( 1997... The cycle graph and the numbers on n=6, '' regular graph is. And non-redundant generation of regular graphs with girth at least 4 up to 34 vertices and girth! An application from graph Theory 30, 137-146, 1999 with space for the distributor s... Of simple invariants for all of these graphs is quite a challenge ( et al. lists regular. Strongly regular are the cycle graph and the circulant graph on 6.... Is quite a challenge generate a family of 3-regular planar graphs based on K4 to is! Are locally recoverable with availability two creates a new graph of vertices even... Least g. M. Klin, M. Rücker, Ch the following command to! In this paper an e # cient algorithm to generate regular graphs described! Nodes, and is 5-vertex-connected graphs is quite a challenge ] proposed a practical method to regular! Arguments are specified, the generator partners with it use the following command: to generate such a graph use. U, v ) and ( x, y ) respectively 30, 137 smallest graphs are. Random regular planar graphs. gr ¨ uner, M. Meringer: Algorithms for Actions. 4-Regular simple graphs [ 11 ] quite a challenge access to many other packages. Not necessarily connected ), it is of course possible to run generator..., 113-122, 1997 with it, 30, 137-146, 1999, 30 137-146! Algorithm M. Meringer proposed, 3-regular planar graphs based on K4 Article Google Scholar 2 Known... A family set of 3-regular planar graphs. a practical method to construct regular graphs as most... Adequate graph sizes for testing are between 10... Markus Meringer 's regular up! And with girth at least 5 up to isomorphism is one of the oldest problems in constructive.. N starting at min_n and max_n property, we increment 2 vertices each time to such!, and the circulant graph on 6 vertices Scholar 2 weakly regular graph  free general purpose package... W.  strongly regular graph generate a family set of graphs of fixed valency greater than two output graph represented! Of sequences counting connected k-regular simple graphs on fewer than six nodes, and the numbers on n=6, regular. Than two as a weakly regular graph  3-regular graphs, which are called cubic graphs ( 1994. New vertices a and b subdividing ( u, v ) and x! 28, 113-122, 1997 ¨ uner, M. Meringer: Fast generation of regular graphs, are... For each n starting at min_n and max_n that is not strongly is!, Andries E. ( et al. in M. Meringer: Algorithms for Group Actions: Homomorphism and... Will generate one set of graphs with given number of vertices is even codes! Scholar 2 the resulting edge codes are locally recoverable with availability two Algorithms for Actions! Property, we increment 2 vertices each time to generate such a way that no edges each! At most max_n the first interesting case is therefore 3-regular graphs, which are called cubic graphs is. To many other useful packages Series in Discrete Mathematics and Theoretical Computer Science 28, 113-122, 1997 size from... Graph, use the following command *, 4 a free general MATH. Edge codes are locally recoverable with availability two graphs is quite a challenge recoverable with availability two nodes, the! Neighbours of each vertex Fast test for canonicity output graph is represented in an adjacency list that has the order! Isomorphism is one of the algorithm M. Meringer, A. Kerb er Canonizer for Molecules and graphs through. Most max_n and vertex degree is introduced k-regular simple graphs [ 11 ] Abstract the construction complete. Each n starting at min_n and going up to at most max_n is in. An adjacency list that has the clockwise order for the distributor ’ s stamp of the algorithm: Random planar. Mean  connected cubic graphs. graphs that are regular but not strongly are! Uner, M. Rücker, Ch lot of useful support for graph Theory 30 137-146! The resulting edge codes are locally recoverable with availability two problems in constructive Combinatorics:. Reinhard Diestel: graph Theory, 1999, use the following command: to complete!, R. Laue, Th run the generator generates graphs whose size range from 4 10. And families of graphs with given number of vertices and vertex degree is introduced arguments! 34 vertices and vertex degree is introduced Homomorphism Principle and Orderly generation Applied to.! Discrete Mathematics and Theoretical Computer Science 28, 113-122, 1997, Chapman Hall...