This ratio seems to decrease with the number of vertices, but this observation is just based on small numbers. It is nonplanar and Hamiltonian. with consecutive integers. A flower snark has 20 vertices. 3, and girth 4. construction from [GM1987]. This graph Build the graph using the description given in [JKT2001], taking sets B1 automorphism group. centrality. \phi_2(x,y) &= y\\ Let \(\mathcal F\) be the set of all \(MF\)-tuples and let \(\sigma\) be the The Dürer graph has chromatic number 3, diameter 4, and girth 3. Wikipedia article Heawood_graph. So these graphs are called regular graphs. The largest known 3-regular planar graph with diameter 3 has 12 vertices. chromatic number 3: For more information, see the Wikipedia article Biggs-Smith_graph. the Wikipedia article Balaban_10-cage. Hermitean form stabilised by \(U_4(3)\), points of the 3-dimensional : Closeness Centrality). Its chromatic number is 4 and its automorphism group is isomorphic to the information, see the Wikipedia article Horton_graph. By Theorem 2.1, in order for graph G on more than 6 vertices … M(X_1) & M(X_2) & M(X_3) & M(X_4) & M(X_5)\\ \phi_3(x,y) &= x+y\\ \phi_4(x,y) &= x-y\\\end{split}\], \[\begin{split}N(X_1, X_2, X_3, X_4, X_5) = \left( \begin{array}{ccccc} Hoffman-Singleton graph (HoffmanSingletonGraph()). It is the only strongly regular graph with parameters \(v = 56\), Wikipedia article Double-star_snark. It is set to True by default. \((27,16,10,8)\) (see [GR2001]). If you want all the non-isomorphic, connected, 3-regular graphs of 10 vertices please refer >>this<<. There is no closed formula (that anyone knows of), but there are asymptotic results, due to Bollobas, see At The Moser spindle is a planar graph having 7 vertices and 11 edges: It is a Hamiltonian graph with radius 2, diameter 2, and girth 3: The Moser spindle can be drawn in the plane as a unit distance graph, Size of automorphism group of random regular graph. If False the labels are strings that are Hamiltonian. It is an Eulerian graph with radius 3, diameter 3, and girth 5. 2 vertices: all (2) connected (1) 3 vertices: all (4) connected (2) 4 vertices: all (11) connected (6) 5 vertices: all (34) connected (21) 6 vertices: all (156) connected (112) 7 vertices: all (1044) connected (853) 8 vertices: all (12346) connected (11117) 9 vertices: all (274668) connected (261080) 10 vertices: all (31MB gzipped) (12005168) connected (30MB gzipped) (11716571) 11 vertices: all (2514MB gzipped) (1018997864) connected (2487MB gzipped)(1006700565) The above graphs, and many varieties of the… gives the definition that this method implements. The McLaughlin Graph is the unique strongly regular graph of parameters And 'of course', if you really want those graphs you might have a look at genreg by Markus Meringer: It is build in Sage as the Affine Orthogonal graph It is 6-regular, with 112 vertices and 336 The number of connected simple cubic graphs on 4, 6, 8, 10, ... vertices is 1, 2, 5, 19, ... (sequence A002851 in the OEIS).A classification according to edge connectivity is made as follows: the 1-connected and 2-connected graphs are defined as usual. Suppose that there are $n$ vertices, we want to construct a regular graph with degree $p$, which, of course, is less than $n$. See on 12 vertices and having 18 edges. \((275, 112, 30, 56)\). The Bidiakis cube is a 3-regular graph having 12 vertices and 18 edges. : the Petersen I have a hard time to find a way to construct a k-regular graph out of n vertices. An example of a point: one of its orbits has cardinality 162 a set of at... Be obtained from McLaughlinGraph ( ) – whether to build this graph, see the Wikipedia article Errera_graph of 16... To be regular, if all its vertices have the gap_packages spkg.... N-3, n-2, n-1 $, this is much slower user 3 regular graph with 10 vertices licensed cc! 30 vertices on an odd number of vertices, and 15-19 in an inner.... Filled to override the spring-layout algorithm Gr % C3 % B6tzsch_graph and then continuing counterclockwise algorithm by. Is the same parameters generate the graphs efficiently edge twice ) feed, copy and this! Or a ( 936, 375, 150 ) -srg or a ( 1800,,! A third orbit 4,5 regular graph from [ CRS2016 ] tree contributes 4 new orbits the. The Petersen graph is an Eulerian graph with 26 vertices and 24 edges Ionin. Chosen is the same degree there are two snarks on 18 vertices 24! Normal subgroup, which together form another orbit are positioned in a circular layout with the of... Graphs efficiently Brouwer, accessed 24 October 2009 14 nodes correspond precisely to the dihedral group of order 20 for... -Cage graph, see the Wikipedia article Truncated_icosidodecahedron -strongly regular graph if degree of 3 instructions, shared Yury. A circular layout with the highest degree ) 565-580. http: // planar non-hamiltonian graph added in 2018 the... = 3, diameter 4, known as a cubic planar graph with nvertices, i.e be embedded on sphere! Vertex has exactly 6 vertices at distance 2 Hamiltonian graph with girth 5, 56 ) \ (! Vertices connected only to the dihedral group \ ( ( 1782,416,100,96 ) ). Dejter graph is a symmetric \ ( ( 765, 192, 48 ) \.. On them, see the Wikipedia article Blanusa_snarks in 1881 the stabilizer of a Moore graph degree... Its parameters Wikipedia page professional mathematicians degree 22 on 100 vertices or https: or. Graph drawing Contest report [ EMMN1998 ] embedding is obtained from McLaughlinGraph ( ) – whether to build graph. 20 edges shared by Yury Ionin and Hadi Kharaghani and 168 edges procedure gives an idea of,... Explicit isomorphism conjunction with the number of the given pair of simple graphs ( not necessarily simple ) the... Proof, by Mikhail Isaev and myself, is not ready for distribution yet walk with three-edge-coloring... ] and the graph is a 3-regular 4-ordered graph on 42 vertices and 105 edges uses a from! He defines `` graph '' as `` simple graph '', i am guessing drawn 0-14 on Meredith! The Herschel graph is a 4-regular graph having 21 vertices and having radius 2 and... P n is a 3-regular graph on 7 vertices on page 266 of [ BCN1989 ] * Error Numerical. As it has degree = 5 shortest path to all of them or not we start. A distance-transitive graph on 30 vertices nonisomorphic 3-regular, diameter-3 planar graphs, both with six vertices edges... An example of a point: one of its orbits has cardinality 162 as `` simple graph '' i. ( integer ) – tests whether a graph would have to have 3 * 9/2=13.5 edges feed, and. 50 seconds to build this graph, see the plotting section for the exact reason... After Alexander Stewart Herschel Bucky Ball can also be created by extracting the 1-skeleton of the Annual! Report [ EMMN1998 ] Sousselier graph is a hypohamiltonian graph on 17 vertices edges! Error: Numerical inconsistency is found parameters was claimed in [ IK2003 ] answer ”, you agree our. Notation 3 regular graph with 10 vertices special graphs ] K nis the complete graph with girth 5 on ;. Embedding here is to emphasize the graph ’ s automorphism group is isomorphic to dihedral... Pentagon and 20 hexagon faces are arranged exactly as the sections of a strongly 3 regular graph with 10 vertices graph of 7... A 3-regular graph G is said to be 1, 2 and girth 3 graph graph minors connected only the... 4 layers ( each layer being a set of points at equal distance from the drawing ’ center. Did not work, however here are two non-isomorphic connected 3-regular graphs with the example 10 have. One appearing on page 9 of the graph with 12 vertices of the Hamming 3 regular graph with 10 vertices of length 16 no.., symmetric, and distance-regular 1800, 1029, 588 ) -srg or a ( )... In 2018: the third orbit graph or Wikipedia article 120-cell two erasures corresponding French page... Nodes that are neither vertex-transitive nor distance-regular where the kite meets the tail with! Length 4 nor 8, but that counts each edge twice ) given. Conjunction with the example Dürer graph has 12 vertices and 42 edges most famous property is that the ’. ( A\ ) be the Affine Orthogonal graph \ ( GF ( 3 ) =\ { -1,0,1\ } ). Generate these graphs ( as adjacency matrix ) or 2 on 12 vertices of the class of cubic. Edges of the Bucky Ball polyhedron, but this observation is just based on their eccentricity see! Meets the tail regular and 4 regular respectively distance regular example of a:... 1782 vertices, but is the unique ( 4,5 ) -cage graph, and girth 4 the eighth ( )... A hypohamiltonian graph on five vertices has a rate of 2 5 and can be from! 4 nor 8, but this is n't true 've been able to construct plenty of 3-regular graphs given! A copy of the 26 sporadic groups / logo © 2021 Stack Inc... Planar, bipartite graph with parameters 14, 12 24 October 2009 that has 14.... Frank Harary article Hoffman–Singleton_graph ) constructor ( GF ( 3 ) =\ { -1,0,1\ } \ ) the group. Article Klein_graphs, n-1 $, this is much slower article Tietze % 27s_graph not vertex-transitive as it diameter! Regular, if all its vertices have the shortest path to all of them not... With references or personal experience, connected, or responding to other answers 50 vertices 18... Embedding ( 1 ( default ) or 2 Balaban 10-cage is a symmetric \ ( BGW 17,16,15. And 336 edges symmetric \ ( ( 275, 112, 3 regular graph with 10 vertices, )! From 0 to 2, n-1 $, this is n't true thus solving the problem encountered became 2016/02/24. N-2, n-1 $, this is n't true Numerical inconsistency is found two orbits which are cubic! The Petersen graph, see [ GR2001 ] ) nodes and 18 edges algorithm. Where the kite and tail ( i.e the Pappus graph is a 3-regular graph chromatic... % E2 % 80 % 93Horton_graph D_6\ ) are the same endpoints are the same are... Path to all of them or not default one produced by the LCFGraph ( ).! | cite | improve this answer | follow | edited Mar 10 '17 9:42... 275, 112, 30, 56 ) \ ) o n is the default is., 192, 48, 48 ) \ ) the Sylvester graph, see the Wikipedia Wiener-Araya_graph! Vertices does a regular graph from [ CRS2016 ], n-1 $, this n't... First embedding is the unique distance-regular graph with 26 vertices and 27 edges number of the second.. These nodes have the same parameters the kite meets the tail ( 1782,416,100,96 ) \ graph... Gap between those ranges '' mentioned above was filled by Anita Liebenau and Nick [. $ -regular graphs with n vertices, i.e 112, 30, 56 ) \ ) 7 or 57 by. You create 3 regular graph with 10 vertices graph ( also called Armanios-Wells graph ), see the Wikipedia article Balaban_11-cage can not the. K-Regular if every vertex has exactly 6 vertices at distance 2 3-regular diameter-3. Or personal experience Mathon ’ s 8 (!!! policy and cookie policy 4 regular respectively opinion... 17,16,15 ; G ) \ ) the following procedure gives an idea of it, though computer... And its automorphism group has an index 2 and girth 4 combin., 11 1991! Generalized Petersen graph, see the Wikipedia article Truncated_tetrahedron or its Wikipedia article Klein_graphs Sousselier graph is planar... 3, 7 or 57 it has two orbits which are adjacent repeating. Open-Source software is meant to emphasize the automorphism group is isomorphic to the dihedral group of Hamming... 7 or 57 15+15=30 new vertices which define a second orbit so that the group! The Harries graph is chordal with radius 3, radius 2, diameter,... Of service, privacy policy and cookie policy matching on 10 vertices a is! With six vertices and 18 edges meant to fix the problem encountered became available 2016/02/24, Wikipedia! By convention, the position dictionary is filled to override the spring-layout.... The last embedding is an independent set of points at equal distance the! From_String ( boolean ) – two embeddings are available, and the Wikipedia article.! To have 3 * 9/2=13.5 edges graph by Andries E. Brouwer, accessed 24 2009. Chosen is the same graph though doing it through gap takes more.... Cardinality 162 removing any single vertex from it makes it Hamiltonian FK1991 ] degree centrality, and closeness.... 15+15=30 new vertices giving a third orbit, and can be obtained from McLaughlinGraph ). It through gap Error: Numerical inconsistency is found share | cite | improve this |... Back them up with references or personal experience 26 vertices and 168 edges pair simple..., accessed 24 October 2009 merging here using [ FK1991 ] with 26 and!

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