Prime Order Element Graph of a Group -- II

2025/08/08 by Tapa Manna, S. Poddar, Manna, Tapa +5
Computer Science · Mathematics · #Matrix Theory and Algorithms #Finite Group Theory Research #Advanced Graph Theory Research

paper · pdf · doi:10.48550/arxiv.2508.06222

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.

Citations

• Forbidden Subgraphs of Prime Order Element Graph
• Graphs defined on groups
• The diameter of the commuting graph of a finite group with trivial centre

Related

• On a new graph defined on the order of elements of a finite group
• Forbidden Subgraphs of Prime Order Element Graph
• The co-prime order graph associated with a finite group
• Characterization of some alternating groups by order and the largest element order
• The non-two-primes graph of a finite group