The digraphs arising by the power maps of generalized quaternion groups

Abstract

We attach a diagraph with generalized Quaternion group of order [Formula: see text] by utilizing the power map [Formula: see text] defined by [Formula: see text] for all [Formula: see text], where [Formula: see text] is a fixed natural number. We examine the structure of these power digraphs and establish numerous results encapsulating the existence of cycle vertices, derivation of different formulae concerning the number of cycles, length of cycles and most importantly in-degree of vertices. Moreover, we categorize the regular and semi-regular power digraphs.