University of KashanMathematics Interdisciplinary Research2538-36397420221201The Non-Coprime Graph of Finite Groups3853948741410.22052/mir.2019.172393.1117ENGholamrezaAghababaei-BeniDepartment of Pure Mathematics,
International Campus of Ferdowsi University of Mashhad,
Mashhad, IranAbbasJafarzadehDepartment of Mathematics,
Quchan University of Technology,
Quchan, 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_f4e8b2a7b27daf1345a4bdf277419ede.pdf