JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (12): 151-160.doi: 10.6040/j.issn.1671-9352.0.2022.316

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Characterizing properties of (signless) Laplacian permanental polynomials of bicyclic graphs

Tingzeng WU*(),Tian ZHOU   

  1. School of Mathematics, Qinghai Minzu University, Xining 810007, Qinghai, China
  • Received:2022-05-17 Online:2023-12-20 Published:2023-12-19
  • Contact: Tingzeng WU E-mail:mathtzwu@163.com

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Abstract:

Let G be a graph with n vertices, and let L(G) and Q(G) be the Laplacian matrix and signless Laplacian matrix of G, respectively. The polynomial π(L(G); x)=per(xI-L(G)) (resp. π(Q(G); x)=per(xI-Q(G))) is called Laplacian permanental polynomial (resp. signless Laplacian permanental polynomial) of G. In this paper, we show that two classes of bicyclic graphs are determined by their (signless) Laplacian permanental polynomials.

Key words: permanent, (signless) Laplacian matrix, (signless) Laplacian permanental polynomial, (signless) Laplacian copermanental

CLC Number: 

  • O157.6

Fig.1

Bycyclic graps d(p, q, r) and θ(p, q, r)"

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