# Dihedral Cayley directed strongly regular graph

#### 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* = 4*w* +2, then we construct a family of DSRGs with parameters * v* = 8*w* + 4, *k* = 4*w*, * t* = 2*w*, μ = 2*w*, and λ = 2*w* − 2 utilizing Cayley graphs of dihedral groups D* _{2n}*. ^

#### 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