Hoffman-singleton graph
NettetThe Hoffman-Singleton graph HS may be described as the unique MOORE graph of degree 7 and diameter 2 [2], or as the unique 7-regular graph of order 50 with girth 5 [1, p. 189]. It may be constructed as follows, where a hep-tad is a set of seven triples which may be taken as the lines of a Fano plane whose Nettet1. feb. 2016 · Hoffman–Singleton Graph – Félix de la Fuente. This is the Hoffman–Singleton graph, a remarkably symmetrical graph with 50 vertices and 175 …
Hoffman-singleton graph
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Nettet24. mar. 2024 · Hoffman-Singleton Theorem. Let be a -regular graph with girth 5 and graph diameter 2. (Such a graph is a Moore graph ). Then, , 3, 7, or 57. A proof of this … Nettet18. mai 2013 · Hoffman-Singleton graph. We’ve shown that there exist graphs of degree 2 and 3 with these properties. The next graph has degree 7, and is known as the …
In the mathematical field of graph theory, the Hoffman–Singleton graph is a 7-regular undirected graph with 50 vertices and 175 edges. It is the unique strongly regular graph with parameters (50,7,0,1). It was constructed by Alan Hoffman and Robert Singleton while trying to classify all Moore graphs, and is the … Se mer Here are two constructions of the Hoffman–Singleton graph. Construction from pentagons and pentagrams Take five pentagons Ph and five pentagrams Qi … Se mer The automorphism group of the Hoffman–Singleton graph is a group of order 252,000 isomorphic to PΣU(3,5 ) the semidirect product of the projective special unitary group PSU(3,5 ) with the cyclic group of order 2 generated by the Frobenius automorphism. … Se mer There are 1260 5-cycles and 5250 6-cycles in the Hoffman–Singleton graph. There are 525 copies of the Petersen graph, … Se mer • McKay–Miller–Širáň graphs, a class of graphs including the Hoffman–Singleton graph • Table of the largest known graphs of a given diameter and maximal degree Se mer NettetThe Hoffman-Singleton graph is the unique Moore graph of order 50, degree 7, diameter 2 and girth 5. A number of different constructions of the graph can be found for example in [1–5, 8], McKay et al. [10] showed that the Hoffman-Singleton graph fits into a family of
NettetHoffman–Singleton graph (Q3090387) From Wikidata. Jump to navigation Jump to search. node-link graph with 50 vertices and 175 edges, the smallest possible 7-regular graph of girth 5. edit. Language Label Description Also known as; English: Hoffman–Singleton graph. Nettet1. jan. 1993 · The Hoffman-Singleton graph is {C 3 , C 4 }-free and attains the upper bound on f (50) from Theorem 2.2. The uniqueness of the graph was shown in [14], [15], and by Cong and Schwenk in [18].
Nettet5. apr. 2013 · We also obtain two new strongly regular graphs. A (finite) partial geometry with parameters s, t and α is a 1 - (v, s + 1, t + 1) design (for which we speak of lines …
In graph theory, a Moore graph is a regular graph whose girth (the shortest cycle length) is more than twice its diameter (the distance between the farthest two vertices). If the degree of such a graph is d and its diameter is k, its girth must equal 2k + 1. This is true, for a graph of degree d and diameter k, if and only if its number of vertices equals an upper bound on the largest possible number of vertices in any graph with this degree and dia… marco pizza rock hill scNettetThe Higman-Sims graph can be constructed from the Hoffman-Singleton graph by treating the latter's 100 independent vertex sets of size 15 as vertices and connecting … csuohio addressNettet15. mar. 2024 · Majorana Algebra for the Hoffman-Singleton Graph. Andries E. Brouwer, Alexander A. Ivanov. Majorana theory is an axiomatic tool introduced by A. A. Ivanov in … csuohio commencementNettetホフマン–シングルトングラフとは、50個の頂点と175個の辺からなる7-正則グラフである。 これは(50,7,0,1)-強正則グラフであり一意である。このグラフはアラン・ホフマン … marco pizza shreveportNettet19. nov. 2024 · In 1960, Alan Hoffman and Robert Singleton examined those expressions when applied on Moore graphs that have λ = 0 and μ = 1. Such graphs are free of triangles (otherwise λ would exceed zero) and quadrilaterals (otherwise μ would exceed 1), hence they have a girth (smallest cycle length) of 5. marco pizzasNettettriad_graph. #. Returns the triad graph with the given name. Each triad name corresponds to one of the possible valid digraph on three nodes. The name of a triad, as described above. The digraph on three nodes with the given name. The nodes of the graph are the single-character strings ‘a’, ‘b’, and ‘c’. marco pizza shreveport laNettetgraph_atlas# graph_atlas (i) [source] # Returns graph number i from the Graph Atlas. For more information, see graph_atlas_g(). Parameters: i int. The index of the graph from the atlas to get. The graph at index 0 is assumed to be the null graph. Returns: list. A list of Graph objects, the one at index i corresponding to the graph i in the ... marco pizza shakopee mn