The Non-Coprime Graph of Finite Groups

Abstract

The non-coprime graph Π_G of a finite group G is a graph with the vertexset G-{e}, where two distinct vertices u and v are adjacent if they havenon-coprime orders. In this paper, the main properties of the Cartesian andtensor product of the non-coprime graph of two finite groups are investigated.We also describe the non-coprime graph of some special groups including thedihedral and semi-dihedral groups. Some open questions are also proposed.

Keywords

• coprime graph‎
• ‎dihedral group‎
• ‎semi-dihedral group‎
• ‎dicyclic group‎