Integer divisor connectivity graph - Jorf, M.; Oukhtite, L. (Ukrains’kyi Matematychnyi Zhurnal, 2025)
UDC 512.5Let $n$ be a nonprime integer. We introduce a new simple undirected graph and denote it by $MD(n),$ where the vertices are the proper divisors of $n$ and two vertices $x$ and $y$ are adjacent if $xy$ divides $n.$ We explore the connectedness of $MD(n)$ and provide detailed calculations for the degree of each vertex. In addition, we focus on the special case where $n = p^{α},$ where $p$ is a prime positive integer and $α≥ 3$ is a positive integer. For these instances, we explicitly determine the chromatic number $χ$ and the clique number $ω$ of $MD(n).$ Finally, we conclude that $χ(MD(n)) = ω(MD(n)).$