The undirected graph Γ() is the zero-divisor graph of the monogenic semigroup S M with zero. The non-zero vertices i and j of this graph are adjacent whenever + > and gcd(,) = 1, where is the order of Γ(). In this work, we consider some properties of the graph Γ(), such as the diameter, girth, chromatic number and clique. In addition, we show that Γ() is a perfect, well-covered and coprime graph.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.