A. A. Makhnev, D. V. Paduchikh, “Graphs in which neighborhoods of vertices are isomorphic to the Mathieu graph”, Trudy Inst. Mat. i Mekh. UrO RAN, 2012, Volume 18, Number 3,Pages <nobr>155

This article is cited in 2 papers

Graphs in which neighborhoods of vertices are isomorphic to the Mathieu graph

A. A. Makhnev^ab, D. V. Paduchikh^a

^a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
^b Ural Federal University

Abstract: We consider graphs in which neighborhoods of vertices are isomorphic to a strongly regular graph with the second eigenvalue equal to $2$. Amply regular graphs in which neighborhoods of vertices are isomorphic to the Mathieu graph (the strongly regular graph with parameters $(77,16,0,4)$ without triangles) are classified.

Keywords: strongly regular graph, Mathieu graph, locally $X$-graph.

UDC: 519.17

Received: 15.09.2011