A new class of directed strongly regular Cayley graphs over dicyclic groups

Abstract

We endeavored to investigate directed strongly regular Cayley graphs (or DSRCG for short) over dicyclic groups $ \operatorname{Dic}_{4n} = \langle \alpha, \beta\; |\; \alpha^{n} = \beta^4 = 1, \beta^{-1}\alpha\beta = \alpha^{-1}\rangle $, where $ n $ is odd. We derived several DSRCGs over $ \operatorname{Dic}_{4n} $ for $ n $ odd. We then derived a criterion for a certain class of Cayley graph to be directed strongly regular.

Keywords

• directed strongly regular cayley graph
• group algebra
• dicyclic groups