Prime Order Element Graph of a Group -- II

Abstract

In this sequel paper, we continue the analysis of the prime order element graph $\Gamma (G)$ of a finite group $G$, where vertices are elements of $G$ and edges connect distinct elements $x,y$ satisfying $\circ (xy)=p$ for some prime $p$. Our investigation focuses on the adjacency and Laplacian spectra, planarity, and clique number of this graph. We conclude by outlining open issues and potential directions for future investigations.

arXiv comment13 pages, 2 figures