The Non-Coprime Graph of Finite Groups

Document Type: Original Scientific Paper

Authors

1 University of Applied Science Tecnology , P .O. Box 1599665111, Tehran, Iran

2 Department of Pure Mathematics, International Campus of Ferdowsi University of Mashhad, Mashhad, I. R. Iran

10.22052/mir.2019.172393.1117

Abstract

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

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Main Subjects