Commuting graph of non-abelian groups of order $p^n$ with center having $p^{n-2}$ elements

Dilpreet Kaur; Gaurav Kumar; Shivam Tiwari

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arXiv · 2606.24269

Commuting graph of non-abelian groups of order $p^n$ with center having $p^{n-2}$ elements

Dilpreet Kaur·Gaurav Kumar·Shivam Tiwari

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Abstract

Let $G$ be a group. The commuting graph $\zeta(G, V)$ of a group $G$ has a vertex set $V\subseteq G,$ two vertices are connected with an edge if the corresponding elements commute in $G.$ In this article, we study the commuting graphs for the non-abelian $p$-groups of order $p^n$ with center size $p^{n-2}.$ We study detour distance, metric dimension, resolving polynomials, and the spectral properties for these graphs.

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Dilpreet Kaur, Gaurav Kumar, Shivam Tiwari. 2026-06-23. Commuting graph of non-abelian groups of order $p^n$ with center having $p^{n-2}$ elements. https://arxiv.org/abs/2606.24269

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