Edge-regular graphs with regular cliques
Gary R. W. Greaves, Jack H. Koolen
TL;DR
This paper presents infinitely many examples of edge-regular graphs with regular cliques that are not strongly regular, answering a longstanding question in graph theory from 1981.
Contribution
It provides the first infinite family of such graphs, expanding understanding of the structure of edge-regular graphs.
Findings
Existence of infinitely many edge-regular graphs with regular cliques
These graphs are not strongly regular
Answers a question posed by Neumaier in 1981
Abstract
We exhibit infinitely many examples of edge-regular graphs that have regular cliques and that are not strongly regular. This answers a question of Neumaier from 1981.
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