Integer divisor connectivity graph - Jorf, M.; Oukhtite, L. (Ukrains’kyi Matematychnyi Zhurnal, 2025)
UDC 512.5 Let 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)).