Dihedral Cayley directed strongly regular graph
A graph is a directed strongly regular graph (DSRG) if and only if the number of paths of length 2 from x to y is: λ, if there is an edge from x to y; μ, if there is not an edge from x to y (with x not equal to y); and t, if x = y. For every vertex in G, the in-degree and out-degree is k. The number of vertices in G is denoted by v. If G is a group and S a subset of G, then the Cayley graph, C(G, S), is the directed graph whose vertices are elements of G, and directed edges are (g, sg) for every g in G and every s in S. ^ If w is any natural number and n = 4w +2, then we construct a family of DSRGs with parameters v = 8w + 4, k = 4w, t = 2w, μ = 2w, and λ = 2w − 2 utilizing Cayley graphs of dihedral groups D2n. ^
Gamez, Jose Jonathan, "Dihedral Cayley directed strongly regular graph" (2012). ETD Collection for University of Texas, El Paso. AAI1512570.