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Hoffman singleton graph

Nettet6. sep. 2013 · The 50-vertex 7-regular Hoffman-Singleton graph; A particular 3250-vertex 57-regular graph whose existence and uniqueness are unknown. Intriguingly, the Hoffman-Singleton theorem has reduced the problem of finding all graphs with this property to a finite case-bash, but where ‘finite’ is still prohibitively large for an … Nettet24. mar. 2024 · For a connected graph G of graph diameter d, the distance-k graph G_k for k=1, ..., d is a graph with the same vertex set and having edge set consisting of the pairs of vertices that lie a distance k apart. It is therefore the case that G_1=G. Distance graphs of interest (because they are distance-regular) include the distance-2 graphs …

File:Hoffman-Singleton graph.svg - Wikipedia

Nettet1. jan. 1980 · PDF On Jan 1, 1980, W. H. Haemers published A new partial geometry constructed from the Hoffman-Singleton graph Find, read and cite all the research you need on ResearchGate NettetThe pentagon, the Petersen graph, and the Hoffman-Singleton graph are all very highly symmetric graphs, and much of the interest in these objects is related to exceptional phenomena in small finite groups. In contrast to this, Higman proved that a 57-regular Moore graph cannot be vertex transitive (see [C]). black eyes in christmas tree https://ayscas.net

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NettetThe Hoffman-Singleton graph is the graph on 50 nodes and 175 edges that is the only regular graph of vertex degree 7, diameter 2, and girth 5. It is the unique -cage graph … 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 … Nettet18. des. 2024 · These optimal graphs, many of which are newly discovered, may find wide applications, ... Hoffman, A.J.; Singleton, R.R. On Moore Graphs with Diameters 2 and 3. In Selected Papers of Alan J Hoffman; World Scientific: Singapore, 2003; pp. 377–384. [Google Scholar] black eyes icd 10

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Hoffman singleton graph

Hoffman-Singleton Theorem -- from Wolfram MathWorld

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 … 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. okt. 2024 · The Hoffman–Singleton graph (diameter 2, girth 5, degree 7, order 50) A hypothetical graph of diameter 2, girth 5, degree 57 and order 3250, whose existence … Nettet21. aug. 2024 · I need ideas on how to draw the Hoffman Singleton graph in LaTeX. Stack Exchange Network Stack Exchange network consists of 181 Q&A communities …

NettetUp Hoffman-Singleton graph There is a unique strongly regular graph Γ with parameters v = 50, k = 7, λ = 0, μ = 1. The spectrum is 7 1 2 28 (–3) 21.. It was found by Hoffman … Nettet3. nov. 2004 · In particular, ford=7 we obtain as a special case the Hoffman–Singleton graph, and ford=11 andd=13 we have new largest graphs of diameter 2, and degreedon 98 and 162 vertices, respectively.

NettetThe -cage is the cycle graph , the -cage is the multigraph of edges on two vertices, the -cage is the complete graph , and the -cage is the bipartite graph . Let be the number of vertices in the -cage graph. Then the following table summarizes exactly known values of for small values of and from 3 to 7. The value was found by McKay et al. (1998). NettetIn our work, we give a straightforward counting argument showing that the Hoffman-Singleton graph answers this question in the affirmative for the case of girth 5. It is then shown that certain generalized polygons, constructed of sufficiently large order, are also PRCF-bad, thus proving the existence of PRCF-bad graphs of girth 6, 8, 12, and 16.

NettetThe Petersen graph is one of the Moore graphs (regular graphs of girth 5 with the largest possible number k 2 + 1 of vertices). Two other Moore graphs are known, namely the pentagon (k = 2) and the Hoffman-Singleton graph (k = 7). If there are other Moore graphs, they must have valency 57 and 3250 vertices, but cannot have a transitive group.

Nettet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 … game free trênNettet19. aug. 2013 · 1. Divide the group in half. The fifty people in one half must each know at least 20 people in their half. The maximal girth 5 cage graph for 50 vertices is the Hoffman-Singleton graph, with degree 7. If each person knows more than 57 people, a 3 or 4 cycle is also forced. Share. black eyes in animeNettetA. J. Hoffman* R. R. Singleton* On Moore Graphs with Diameters 2 and 3 Abstract: This note treats the existence of connected, undirected graphs homogeneous of degree cI and of diameter Ie, having a number of nodes which is maximal according to a certain definition. For Ie = 2 unique graphs exist for cI = 2, 3, 7 and possiblyfor cI = 57 (which … blackeye smite twitter