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
Symmetry Free Full-Text A Structured Table of Graphs with ...
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