A Note on A Family of Directed Strongly Regular Graphs

A Note on A Family of Directed Strongly Regular Graphs

where J is the all ones matrix and I is the identity. These matrix conditions are equivalent to the combinatorial conditions that the graph is both inand out-regular, and that the number of directed 2-paths from a vertex x to a vertex y is t if x = y, λ if x → y, and μ otherwise. Recently, these graphs were studied by Klin et al. [2], including some new constructions and a list of feasible para...

A Note on Strongly Quotient Graphs

a note on strongly quotient graphs

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On a Family of Diamond-Free Strongly Regular Graphs

The existence of a partial quadrangle PQ(s, t, μ) is equivalent to the existence of a diamond-free strongly regular graph SRG(1+s(t+1)+s2t(t+1)/μ, s(t+1), s−1, μ). Let S be a PQ(3, (n + 3)(n2 − 1)/3, n2 + n) such that for every two non-collinear points p1 and p2, there is a point q non-collinear with p1, p2, and all points collinear with both p1 and p2. In this article, we establish that S exis...

Representations of directed strongly regular graphs

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.