The integral circulant graph ICGn(D) has the vertex set Zn = {0, 1, 2, . , n? 1} and vertices a b are adjacent if gcd(a ? b, n) D, where D Dn, Dn {d : d | n, 1 < n}. Motivated by incorrect proof of previously published result, in this paper we characterize class graphs that strongly regular. More precisely, connected is regular only n composite m d} for some 2.

We construct two-intersection sets in PG(5, q), q odd, admitting PSL(2, q), whose associated strongly regular graphs have the same parameters as, but are not isomorphic to, Paley graphs.

We consider the following generalization of strongly regular graphs. A graph G is a Deza graph if it is regular and the number of common neighbors of two distinct vertices takes on one of two values (not necessarily depending on the adjacency of the two vertices). We introduce several ways to construct Deza graphs, and develop some basic theory. We also list all diameter two Deza graphs which a...

A directed strongly regular graph with parameters (n, k, t, λ, μ) is a k-regular directed graph with n vertices satisfying that the number of walks of length 2 from a vertex x to a vertex y is t if x = y, λ if there is an edge directed from x to y and μ otherwise. If λ = 0 and μ = 1 then we say that it is a mixed Moore graph. It is known that there are unique mixed Moore graphs with parameters ...