Structural and spectral properties of unitary Haar graphs

Abstract

Let [Formula: see text] and [Formula: see text] be the multiplicative group of the additive group [Formula: see text] of integers modulo [Formula: see text]. The unitary Haar graph [Formula: see text] is a graph with vertex set [Formula: see text] and the edge set [Formula: see text]. In this paper, we study some structural properties of [Formula: see text] such as total chromatic number, diameter, planarity, the girth, vertex-connectivity and edge-connectivity. Also, some spectral properties of the graph [Formula: see text] are determined.