Dihedral Cayley directed strongly regular graph

Jose Jonathan Gamez, University of Texas at El Paso

Abstract

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.

Subject Area

Mathematics

Recommended Citation

Gamez, Jose Jonathan, "Dihedral Cayley directed strongly regular graph" (2012). ETD Collection for University of Texas, El Paso. AAI1512570.
https://digitalcommons.utep.edu/dissertations/AAI1512570

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