The Zero-Divisor Graphs of Variation Monogenic Semigroups

(Bana Al Subaiei and Abolape Deborah Akwu)

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Abstract

The undirected graph Γ(〖VS〗_Mn) is the zero-divisor graph of the monogenic semigroup SM with zero. The non-zero vertices xi and xj of this graph are adjacent whenever i + j > n and gcd⁡(i,j)=1, where n is the order of Γ(〖VS〗_Mn). In this work, we consider some properties of the graph Γ(〖VS〗_Mn ), such as the diameter, girth, chromatic number and clique. In addition, we show that Γ(〖VS〗_Mn ) is a perfect, well-covered and coprime graph.

KEYWORDS
Diameter, girth, chromatic number, clique, relative prime numbers, adjacency

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