The properties of the Laplacian permanental polynomials of graphs

Wei Li; Wei Li

doi:10.3934/math.20251078

AIMS Mathematics

2025, Volume 10, Issue 10: 24317-24328. doi: 10.3934/math.20251078

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Research article

The properties of the Laplacian permanental polynomials of graphs

Wei Li ^{1,2
,
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1.
Research & Development Institute of Northwestern Polytechnical University in Shenzhen, Shenzhen, Guangdong 518057, China
2.
School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an, Shaanxi, 710129, China

Received: 26 February 2025 Revised: 11 June 2025 Accepted: 02 July 2025 Published: 24 October 2025
MSC : 05C31

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.
- Laplacian permanental polynomial,
- permanental polynomial
Citation: Wei Li. The properties of the Laplacian permanental polynomials of graphs[J]. AIMS Mathematics, 2025, 10(10): 24317-24328. doi: 10.3934/math.20251078

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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.

References

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