Prime Order Element Graph of a Group -- II

In this sequel paper, we continue the analysis of the prime order element graph $\mathrm{\Gamma }(G)$ 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.