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Research Article | Open Access

The properties of the Laplacian permanental polynomials of graphs

Wei Li1,2( )
Research & Development Institute of Northwestern Polytechnical University in Shenzhen, Shenzhen, Guangdong 518057, China
School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an, Shaanxi, 710129, China
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Abstract

In this paper, some properties of the Laplacian permanental polynomials of graphs are given. First, we provide a formula to evaluate the coefficients of the Laplacian permanental polynomial. Following this, we derive some interesting derivative properties of the Laplacian permanental polynomial. In addition, the recursive relations on the Laplacian permanental coefficients of some subdivision graphs are deduced.

Keywords

Laplacian permanental polynomialpermanental polynomial
CLC number: 05C31

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AIMS Mathematics
Volume 10 Issue 10,
October 2025
Pages 24317-24328
DOI: 10.3934/math.20251078

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Li W. The properties of the Laplacian permanental polynomials of graphs. AIMS Mathematics, 2025, 10(10): 24317-24328. https://doi.org/10.3934/math.20251078

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Received: 26 February 2025
Revised: 11 June 2025
Accepted: 02 July 2025
Published: 24 October 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)