Spectrum and energies of commuting conjugacy class graph of a finite group

Document Type : Research Paper

Authors

1 Department of Mathematics, Cachar College, Silchar-788001, Assam, India.

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

Abstract

In this paper we compute spectrum, Laplacian spectrum, signless Laplacian spectrum and their corresponding energies of commuting conjugacy class graph of the group $G(p, m, n) = \langle x, y : x^{p^m} = y^{p^n} = [x, y]^p = 1, [x, [x, y]] = [y, [x, y]] = 1\rangle$, where $p$ is any prime, $m \geq 1$ and $n \geq 1$. We derive some consequences along with the fact that commuting conjugacy class graph of $G(p, m, n)$ is super integral. We also compare various energies and determine whether commuting conjugacy class graph of $G(p, m, n)$ is hyperenergetic, L-hyperenergetic or Q-hyperenergetic.

Keywords

References

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Algebraic Structures and Their Applications

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Available Online from 01 July 2024

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