University of KashanMathematics Interdisciplinary Research2538-3639Articles in Press20181201The Non-Coprime Graph of Finite Groups8741410.22052/mir.2019.172393.1117ENGholam RezaAghababaei-BeniUniversity of Applied Science Tecnology , P .O. Box 1599665111, Tehran, IranAbbasJafarzadehDepartment of Pure Mathematics,
International Campus of Ferdowsi University of Mashhad,
Mashhad, I. R. IranJournal Article20190217The non-coprime graph Π_G of a finite group G is a graph with the vertex<br /> set G-{e}, where two distinct vertices u and v are adjacent if they have<br /> non-coprime orders. In this paper, the main properties of the Cartesian and<br /> tensor product of the non-coprime graph of two finite groups are investigated.<br /> We also describe the non-coprime graph of some special groups including the<br /> dihedral and semi-dihedral groups. Some open questions are also proposed.https://mir.kashanu.ac.ir/article_87414_c6694e468730b72fd183057bc8b8c37a.pdf