Prime Order Element Graph of a Group -- II

Tapa Manna; Sauvik Poddar; Angsuman Das; Baby Bhattacharya

Prime Order Element Graph of a Group -- II

Group Theory 2025-08-11 v1 Combinatorics

Authors: Tapa Manna , Sauvik Poddar , Angsuman Das , Baby Bhattacharya

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.

Keywords

prime order element graph finite group adjacency spectrum Laplacian spectrum planarity clique number

Cite

@article{arxiv.2508.06222,
  title  = {Prime Order Element Graph of a Group -- II},
  author = {Tapa Manna and Sauvik Poddar and Angsuman Das and Baby Bhattacharya},
  journal= {arXiv preprint arXiv:2508.06222},
  year   = {2025}
}

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13 pages, 2 figures

Prime Order Element Graph of a Group -- II

Abstract

Keywords

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