Coprime order graphs of finite Abelian groups and dihedral groups
Volume 23, Issue 3, pp 196202
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 coprime 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 coprime order graph of a finite Abelian group or dihedral group.We also investigate the Laplacian spectrum of the coprime order graph \(\Theta (G)\) when G is a finite Abelian pgroup, \({\mathbb{Z}_p}^t \times {\mathbb{Z}_q}^s\) or a dihedral group \(D_{p^n}\).
Share and Cite
ISRP Style
Amit Sehgal, Manjeet, Dalip Singh, Coprime order graphs of finite Abelian groups and dihedral groups, Journal of Mathematics and Computer Science, 23 (2021), no. 3, 196202
AMA Style
Sehgal Amit, Manjeet, Singh Dalip, Coprime order graphs of finite Abelian groups and dihedral groups. J Math Comput SCIJM. (2021); 23(3):196202
Chicago/Turabian Style
Sehgal, Amit, Manjeet,, Singh, Dalip. "Coprime order graphs of finite Abelian groups and dihedral groups." Journal of Mathematics and Computer Science, 23, no. 3 (2021): 196202
Keywords
 Coprime order graph
 finite Abelian group
 dihedral group
 Laplacian spectrum
MSC
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