The Non-Coprime Graph of Finite Groups

Document Type : Original Scientific Paper

Authors

1 Department of Pure Mathematics, International Campus of Ferdowsi University of Mashhad, Mashhad, Iran

2 Department of Mathematics, Quchan University of Technology, Quchan, Iran

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

References

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the symmetric and alternating groups, J. Algebra Appl. 7(1) (2008) 129–146.
[4] F. Mansoori, A. Erfanian and B. Tolue, Non-coprime graph of a finite group,
AIP Conference Proceedings, 1750 (1) (2016) 050017.
[5] J. S. Williams, Prime graph components of finite groups, J. Algebra, 69 (2)
(1981) 487–513.
Mathematics Interdisciplinary Research
Volume 7, Issue 4
December 2022
Pages 385-394

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