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Hoffman-singleton graph

Nettet14. okt. 2024 · I have a python code need to draw a networkx graph, it can output normally. However, I got some problems in the following code. import networkx as nx import matplotlib.pyplot as plt import matplotl... 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

Hoffman-Singleton graph Complex Projective 4-Space

Nettet19. 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. Nettet15. jun. 2024 · Construction From M22 graph. Take the M22 graph, a strongly regular graph srg(77,16,0,4) and augment it with 22 new vertices corresponding to the points … boxing trophies https://brain4more.com

Hoffman-Singleton Graph -- from Wolfram MathWorld

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 … Nettet15. 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 … Nettet23. apr. 2024 · By the construction of Petersen graph and Hoffman-Singleton graph from block designs, we will give a possible and uniform construction of Moore graphs of diameter 2 in this note. boxing turnbuckle

Hoffman-Singleton graph - Eindhoven University of …

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Hoffman-singleton graph

(PDF) Structure of the Hoffman-Singleton graph - ResearchGate

NettetHoffman AJ, Singleton RR (1960) On moore graphs with diameters 2 and 3. IBM J Res Dev 4(5):497---504 Google Scholar Digital Library; Dally WJ, Towles BP (2004) Principles and practices of interconnection networks. Morgan Kaufmann, Massachusetts Google Scholar Digital Library; Jantsch A, Tenhunen H et al (2003) Networks on chip, vol 396. NettetDownload scientific diagram (a) A construction of the Petersen graph by lifting with the group C5. (b) By lifting the described graph with the group C 2 5 , we get the Hoffman-Singleton graph.

Hoffman-singleton graph

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http://www-math.ucdenver.edu/~wcherowi/courses/m6023/elena.pdf 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 …

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]. NettetThere is a beautiful way to construct the Hoffman–Singleton graph by connecting 5 pentagons to 5 pentagrams. 1 February, 2016 in Graphs, Groups, Images Library. Balaban 11-Cage. This picture shows part of a graph called the Balaban 11-cage. A (3,11)-graph is a simple graph where every vertex has 3 neighbors and the shortest …

NettetThe first number in this sequence, 7, is the degree of the Hoffman–Singleton graph, and the McKay–Miller–Širáň graph of degree seven is the Hoffman–Singleton graph. 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]

NettetIn addition to being a Moore graph, the Hoffman-Singleton graph is part of a family of non-Cayley transitive graphs with order 2q2, where q ≡ 1 (mod 4) is a prime power, which was proved by B. McKay, M. Miller, and J. Siran, so these graphs are termed McKay-Miller-Siran graphs [10]. All the other graphs in this family have girth 3,

Nettet24. mar. 2024 · Hoffman and Singleton (1960) first used the term "Moore graph" while looking at related regular graphs of a given vertex degree and diameter.They showed … boxing turnhoutNettetThe Hoffman–Singleton graph is a symmetrical undirected graph with 50 nodes and 175 edges. All indices lie in Z % 5: that is, the integers mod 5 [1] . It is the only regular … boxing tunesNettetIsSubgraphIsomorphic: test for isomorphism against subgraphs of a graph. IsSubgraphIsomorphic tests whether a given graph is isomorphic to a subgraph of another given graph. This problem is strictly harder than the graph isomorphism problem. Returning to the above example, here we show again that the Sylvester graph is … boxing tubes