On the monoid of partial isometries of a wheel graph

Abstract

In this paper, we consider the monoid [Formula: see text] of all partial isometries of a wheel graph [Formula: see text] with [Formula: see text] vertices. Our main objective is to determine the rank of [Formula: see text]. In the process, we also compute the ranks of three notable subsemigroups of [Formula: see text]. We also describe Green’s relations of [Formula: see text] and of its three considered subsemigroups.