COMMON NEIGHBOURHOOD SPECTRUM AND ENERGY OF COMMUTING CONJUGACY CLASS GRAPH

Document Type : Original Manuscript

Authors

Department of Mathematical Sciences, Tezpur University, Napaam-784028, Sonitpur, India.

Abstract

In this paper, we compute the common neighbourhood (abbreviated as CN) spectrum and the common neighbourhood energy of commuting conjugacy class graph of several families of finite non-abelian groups. As a consequence of our results, we show that the commuting conjugacy class graphs of the groups $D_{2n}$, $T_{4n}$, $SD_{8n}$, $U_{(n,m)}$, $U_{6n}$, $V_{8n}$, $G(p, m, n)$ and some families of groups whose central quotient is isomorphic to $D_{2n}$ or $\mathbb{Z}_p \times \mathbb{Z}_p$, for some prime $p$, are CN-integral but not CN-hyperenergetic.

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References

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Journal of Algebraic Systems
Volume 12, Issue 2
January 2025
Pages 301-326

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