Co-prime order graphs of finite Abelian groups and dihedral groups

Volume 23, Issue 3, pp 196--202 http://dx.doi.org/10.22436/jmcs.023.03.03
Publication Date: November 01, 2020 Submission Date: August 19, 2020 Revision Date: September 23, 2020 Accteptance Date: September 28, 2020

Authors

Amit Sehgal - Department of Mathematics, Pt. NRS Govt. College, Rohtak (Haryana), India. Manjeet - Department of Mathematics, Pt. NRS Govt. College, Rohtak (Haryana), India. Dalip Singh - Department of Mathematics, Maharshi Dayanand University, Rohtak (Haryana), India.


Abstract

The co-prime order graph \(\Theta (G)\) of a given finite group is a simple undirected graph whose vertex set is the group \(G\) itself, and any two vertexes \(x,y\) in \(\Theta (G)\) are adjacent if and only if \(gcd(o(x),o(y))=1\) or prime. In this paper, we derive a precise formula to count the vertex's degree in the co-prime order graph of a finite Abelian group or dihedral group.We also investigate the Laplacian spectrum of the co-prime order graph \(\Theta (G)\) when G is a finite Abelian p-group, \({\mathbb{Z}_p}^t \times {\mathbb{Z}_q}^s\) or a dihedral group \(D_{p^n}\).


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ISRP Style

Amit Sehgal, Manjeet, Dalip Singh, Co-prime order graphs of finite Abelian groups and dihedral groups, Journal of Mathematics and Computer Science, 23 (2021), no. 3, 196--202

AMA Style

Sehgal Amit, Manjeet, Singh Dalip, Co-prime order graphs of finite Abelian groups and dihedral groups. J Math Comput SCI-JM. (2021); 23(3):196--202

Chicago/Turabian Style

Sehgal, Amit, Manjeet,, Singh, Dalip. "Co-prime order graphs of finite Abelian groups and dihedral groups." Journal of Mathematics and Computer Science, 23, no. 3 (2021): 196--202


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