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 $b_1=k-\lambda-1$.