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- W1486443476 abstract "An undirected graph on $v$ vertices in which the degrees of all vertices are equal to $k$ and each edge belongs to exactly $lambda$ triangles is said to be edge-regular with parameters $(v,k,lambda )$. It is proved that an edge-regular graph with parameters $(v,k,lambda )$ such that $kge 3b_1-3$ either has diameter 2 and coincides with the graph $P(2)$ on 20 vertices or with the graph $M(19)$ on 19 vertices; or has at most $2k+4$ vertices; or has diameter at least 3 and is a trivalent graph without triangles, or the line graph of a quadrivalent graph without triangles, or a locally hexagonal graph; or has diameter 3 and satisfies $|Gamma _3(u)|le 1$ for each vertex $u$." @default.
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- W1486443476 date "2007-06-04" @default.
- W1486443476 modified "2023-09-27" @default.
- W1486443476 title "On edge-regular graphs with $kge 3 b_1-3$" @default.
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- W1486443476 doi "https://doi.org/10.1090/s1061-0022-07-00959-4" @default.
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