The Signless Laplacian Spread of Power Graphs of Finite Groups

Year 2025, Volume: 7 Issue: 2, 24 - 35, 30.12.2025

Subarsha Banerjee

https://doi.org/10.54286/ikjm.1658465

Abstract

Given a finite group G, let P(G) denote the power graph of the group G.
Let Q(G) denote the signless Laplacian matrix of a graph G. Moreover, let
λ1 and λn denote the largest and smallest eigenvalues of Q(G). The signless
Laplacian spread of Q(G) is defined as λ1−λn. In this paper, we have described
the signless Laplacian spread of the power graph of the finite cyclic group Zn.
We provide the exact value of the signless Laplacian spread of the power graph
of Zn when n is a power of a prime number, or when n is a product of two
distinct prime numbers. For other forms of n, we provide lower and upper
bounds on the same.

Keywords

Signless Laplacian , spread , power graph

Ethical Statement

The authors declare that there is no conflict of interest. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. This study did not involve human or animal subjects and does not require ethical approval.

Supporting Institution

JIS University

Thanks

The authors thank JIS University for the support and cooperation.

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