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JOURNALS // Trudy Instituta Matematiki i Mekhaniki UrO RAN // Archive

Trudy Inst. Mat. i Mekh. UrO RAN, 2012 Volume 18, Number 3, Pages 90–98 (Mi timm842)

Classification of amply regular graphs with $b_1=6$

K. S. Efimov

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

Abstract: An undirected graph with $v$ vertices in which the degrees of all vertices are equal to $k$, each edge is contained in exactly $\lambda$ triangles, and the intersection of the neighborhoods of any two vertices at distance 2 contains exactly $\mu$ vertices is called amply regular with parameters $(v,k,\lambda,\mu)$. We complete the classification of amply regular graphs with $b_1=6$, where $b_1=k-\lambda-1$.

Keywords: amply regular graph, distance-regular graph.

UDC: 519.17

Received: 13.01.2012


 English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2013, 283, suppl. 1, 46–55

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