On spectra and spectral radius of Signless Laplacian of power graphs of some finite groups

Author:

Banerjee Subarsha1,Adhikari Avishek2

Affiliation:

1. Department of Pure Mathematics, University of Calcutta, 35 Ballygunge Circular Road, Kolkata 700019, West Bengal, India

2. Department of Mathematics, Presidency University, 86, 1, College Street, College Square, Kolkata 700073, West Bengal, India

Abstract

Let [Formula: see text] denote the power graph of a finite group [Formula: see text]. Let [Formula: see text] denote the Signless Laplacian spectral radius of [Formula: see text]. In this paper, we give lower and upper bounds on [Formula: see text] for any [Formula: see text] and find those graphs for which the extremal values are attained. We give a comparison between the bounds obtained and exact value of [Formula: see text] for any [Formula: see text]. We then find the eigenvalues of [Formula: see text] and give lower and upper bounds on the spectral radius of [Formula: see text]. When [Formula: see text] and [Formula: see text] where [Formula: see text] are primes and [Formula: see text] is a positive integer, we obtain sharper bounds on [Formula: see text]. Finally, we make a conjecture on [Formula: see text] for any [Formula: see text].

Funder

National Board for Higher Mathematics

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. On structural and spectral properties of reduced power graph of finite groups;Asian-European Journal of Mathematics;2023-07-12

2. Spectra and Topological Indices of Comaximal Graph of $${\mathbb {Z}}_{n}$$;Results in Mathematics;2022-04-06

3. Prime coprime graph of a finite group;Novi Sad Journal of Mathematics;2021-03-30

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