On prime coprime graphs of certain finite groups

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Document Type : Original paper

Authors

Department of Mathematics, Central University of South Bihar, Gaya–824236, Bihar, India

Abstract

The prime coprime graph $\Theta(G)$ of a finite group $G$ is the graph whose vertex set is $G$ and any two distinct vertices are adjacent if the greatest common divisor of their orders is either $1$ or a prime. In this paper, we investigate Hamiltonicity, clique number, and vertex degree of $\Theta(G)$ for cyclic, dihedral, and dicyclic groups $G$. We establish that $\Theta(G)$ admits a $(k,1)$-partition for cyclic, dihedral, and dicyclic groups $G$ of specified orders.

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References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 26 August 2026

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