In this article we construct a series of new infinite families of strongly regular graphs with the same parameters as the point-graphs of non-singular quadrics in PG(n, 2). We study these graphs, describing and counting their maximal cliques, and determining their automorphism groups.

For strongly regular graphs with adjacency matrix A, we look at the binary codes generated by A and A+ I . We determine these codes for some families of graphs, we pay attention to the relation between the codes of switching equivalent graphs and, with the exception of two parameter sets, we generate by computer the codes of all known strongly regular graphs on fewer than 45 vertices.

Let J3 be the number of vertices commonly adjacent to any pair of non-adjacent vertices. It is proved that every strongly regular graph with even order and J3 ~ 1 is l-extendable. We also show that every strongly regular graph of degree at least 3 and cyclic edge connecti vity at least 3k -3 is 2-extendab Ie. Strongly regular graphs of k even order and of degree k at least 3 with J3 ~"3 are 2-e...

Antipodal covers of strongly regular graphs which are not necessarily distance-regular are studied. The structure of short cycles in an antipodal cover is considered. In most cases, this provides a tool to determine if a strongly regular graph has an antipodal cover. In these cases, covers cannot be distance-regular except when they cover a complete bipartite graph. A relationship between antip...

Directed Strongly Regular Graphs (DSRG) were introduced by Duval as a generalization of strongly regular graphs (SRG’s) [4]. As observed in [8] a special case of these are the doubly regular tournaments or equivalently, the skew Hadamard matrices. As the latter already lead to many interesting codes [10] it is natural to consider the more general case of codes constructed from the adjacency mat...

We present a purely combinatorial construction of strongly regular graphs with geometric parameters. The construction produces hyperexponentially many graphs, and uses neither linear algebra nor groups. Among the graphs constructed, there are graphs with parameters of a generalized quadrangle GQðn 1; nþ 1Þ which further produce distance regular covers of complete graphs. In this paper we presen...

A strongly regular graph with λ = 0 and μ = 3 is of degree 3 or 21. The automorphisms of prime order and the subgraphs of their fixed points are described for a strongly regular graph Γ with parameters (162, 21, 0, 3). In particular, the inequality |G/O(G)| ≤ 2 holds true for G = Aut(Γ).

We develop a theory of representations in Rm for directed strongly regular graphs, which gives a new proof of a nonexistence condition of Jørgensen [8]. We also describe some new constructions.

Andries Brouwer maintains a public database of existence results for strongly regular graphs on n ≤ 1300 vertices. We implemented most of the infinite families of graphs listed there in the open-source software Sagemath [15], as well as provided constructions of the “sporadic” cases, to obtain a graph for each set of parameters with known examples. Besides providing a convenient way to verify t...

A strongly regular graph is called trivial if it or its complement is a union of disjoint cliques. We prove that the parameters n; k; ; of nontrivial strongly regular graphs satisfy = k=n+ o (n) and = k=n+ o (n) : It follows, in particular, that every in…nite family of nontrivial strongly regular graphs is quasi-random in the sense of Chung, Graham and Wilson. 1 Introduction Our graph-theoretic...