Document Type
Lecture
Publication Date
3-4-2015
Abstract
A k-regular graph G of diameter not exceeding two is easily seen to have at most n = 1+k2 vertices. If G has exactly 1 + k2 vertices, it is said to be a Moore Graph. K1K2C5 and the Petersen Graph are Moore Graphs with k = 0123 Homan and Singleton displayed, in 1960, a Moore Graph with k = 7 and they proved that if there is another it must be with k = 57. Their lovely proof uses eigenvalues of the adjacency matrix. I will show the Homan-Singleton proof and then discuss observations by Siemion Fajtlowicz and Bing Wei which may prove useful in constructing the putative Moore graph with k = 57 and n = 3250:
Relational Format
presentation
Recommended Citation
Staton, William, "Moore Graphs of Diameter two: The Homan-Singleton Problem" (2015). Combinatorics Seminar. 41.
https://egrove.olemiss.edu/math_combinatorics/41
