This article is cited in 1 paper

Mathematical logic, algebra and number theory

Edge-symmetric strongly regular graphs with at most 100 vertices

M. S. Nirova

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg

Abstract: Makhnev A.A. and Nirova M.S. remark that from 30 collections of parameters of unknown strongly regular graphs with at most 100 vertices only 11 can respond to edge-symmetric graphs. In this paper it is investigated the possible orders and the structures of subgraphs of the fixed points of automorphisms of strongly regular graph with parameters (100,33,8,12). It is proved that strongly regular graphs with parameters (100,33,8,12) and (100,66,44,42) are not edge-symmetric. As a corollary we have that a new edge-symmetric strongly regular graph with at most 100 vertices does not exist.

Keywords: strongly regular graph, edge-symmetric graph.

UDC: 519.17+512.54

MSC: 05C25

Received December 15, 2012, published January 3, 2013