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October 16, 20250 citationsOpen Access

Prime Order Element Graph of a Group -- II

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TMTapa MannaSPS. PoddarADAngsuman Das

Key Points

  • The study reveals new insights into the adjacency spectra of the prime order element graph of finite groups, indicating underlying structural properties.
  • Key findings indicate a relationship between clique number and the planarity of the prime order element graph, essential for understanding graph structure.
  • This investigation includes a detailed analysis of the Laplacian spectra, providing a deeper understanding of the relationships between group elements.
  • Future directions are proposed based on open issues identified during the analysis of prime order element graphs in finite groups.

Abstract

In this sequel paper, we continue the analysis of the prime order element graph Γ (G) of a finite group G, where vertices are elements of G and edges connect distinct elements x, y satisfying (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.

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Cite This Study

Manna et al. (2025) studied this question.

synapsesocial.com/papers/68f12bfb2107091eab27a2e5https://doi.org/10.48550/arxiv.2508.06222
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