Some properties of the Hoffman-Singleton graph

Citation

Rowlinson P & Sciriha I (2007) Some properties of the Hoffman-Singleton graph. Applicable Analysis and Discrete Mathematics, 1 (2), pp. 438-445. https://doi.org/10.2298/AADM0702438R

Abstract
The Hoffman-Singleton graph, with spectrum 7(1), 2(28), -3(21), is characterized among regular graphs by a star complement for the eigenvalue 2, that is, by an induced subgraph of order 22 without 2 as an eigenvalue. Properties of other induced subgraphs are noted; in particular, the subgraph induced by vertices at distance 2 from a given vertex is the edge-disjoint union of three Hamiltonian cycles.

Keywords
COMPLEMENT; CYCLE; CYCLES; DISTANCE; graph; ORDER; other; properties; SPECTRA; spectrum; star complement

Journal
Applicable Analysis and Discrete Mathematics: Volume 1, Issue 2