The Signless Laplacian Spread of Power Graphs of Finite Groups

Subarsha Banerjee

doi:10.54286/ikjm.1658465

The Signless Laplacian Spread of Power Graphs of Finite Groups

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

Supporting Institution

JIS University

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.

Thanks

The authors thank JIS University for the support and cooperation.

References

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Details

Primary Language

English

Subjects

Combinatorics and Discrete Mathematics (Excl. Physical Combinatorics)

Journal Section

Research Article

Authors

Subarsha Banerjee ^*
0000-0002-7029-7650
India

Publication Date

December 30, 2025

Submission Date

March 15, 2025

Acceptance Date

October 27, 2025

Published in Issue

Year 2025 Volume: 7 Number: 2

DOI

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

IZ

https://izlik.org/JA33BL64GJ

Cite

RIS / Bibtex

APA

Banerjee, S. (2025). The Signless Laplacian Spread of Power Graphs of Finite Groups. Ikonion Journal of Mathematics, 7(2), 24-35. https://doi.org/10.54286/ikjm.1658465

AMA

1.Banerjee S. The Signless Laplacian Spread of Power Graphs of Finite Groups. ikjm. 2025;7(2):24-35. doi:10.54286/ikjm.1658465

Chicago

Banerjee, Subarsha. 2025. “The Signless Laplacian Spread of Power Graphs of Finite Groups”. Ikonion Journal of Mathematics 7 (2): 24-35. https://doi.org/10.54286/ikjm.1658465.

EndNote

Banerjee S (December 1, 2025) The Signless Laplacian Spread of Power Graphs of Finite Groups. Ikonion Journal of Mathematics 7 2 24–35.

IEEE

[1]S. Banerjee, “The Signless Laplacian Spread of Power Graphs of Finite Groups”, ikjm, vol. 7, no. 2, pp. 24–35, Dec. 2025, doi: 10.54286/ikjm.1658465.

ISNAD

Banerjee, Subarsha. “The Signless Laplacian Spread of Power Graphs of Finite Groups”. Ikonion Journal of Mathematics 7/2 (December 1, 2025): 24-35. https://doi.org/10.54286/ikjm.1658465.

JAMA

1.Banerjee S. The Signless Laplacian Spread of Power Graphs of Finite Groups. ikjm. 2025;7:24–35.

MLA

Banerjee, Subarsha. “The Signless Laplacian Spread of Power Graphs of Finite Groups”. Ikonion Journal of Mathematics, vol. 7, no. 2, Dec. 2025, pp. 24-35, doi:10.54286/ikjm.1658465.

Vancouver

1.Subarsha Banerjee. The Signless Laplacian Spread of Power Graphs of Finite Groups. ikjm. 2025 Dec. 1;7(2):24-35. doi:10.54286/ikjm.1658465