Finite Groups Whose Co-prime Order Graphs Have Positive Genus
Keywords:co-prime order graph, genus, finite group
Given a finite group G, the co-prime order graph of G is the simple undirected graph whose vertex set is G, and two distinct vertices x; y are adjacent if gcd(o(x); o(y)) = 1 or p, where p is a prime, and o(x) and o(y) are the orders of x and y, respectively. In this paper, we prove that, for a fixed positive integer k, there are finitely many finite groups whose co-prime order graphs have (non)orientable genus k. As applications, we classify all finite groups whose co-prime order graphs have (non)orientable genus one and two.
How to Cite
LicenseCopyright (c) 2022 Proceedings of the Bulgarian Academy of Sciences
Copyright (c) 2022 Proceedings of the Bulgarian Academy of Sciences
Copyright is subject to the protection of the Bulgarian Copyright and Associated Rights Act. The copyright holder of all articles on this site is Proceedings of the Bulgarian Academy of Sciences. If you want to reuse any part of the content, please, contact us.