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《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (12): 151-160.doi: 10.6040/j.issn.1671-9352.0.2022.316

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双圈图的(无符号)拉普拉斯积和多项式的刻画性质

吴廷增*(),周田   

  1. 青海民族大学数学与统计学院, 西宁 青海 810007
  • 收稿日期:2022-05-17 出版日期:2023-12-20 发布日期:2023-12-19
  • 通讯作者: 吴廷增 E-mail:mathtzwu@163.com
  • 作者简介:吴廷增(1978—), 男, 博士, 教授, 研究方向为图论与组合优化、复杂网络与数据科学.E-mail: mathtzwu@163.com
  • 基金资助:
    国家自然科学基金资助项目(12261071);青海省自然科学基金资助项目(2020-ZJ-920)

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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摘要：

令G为n个顶点的图, L(G)与Q(G)分别表示图G的拉普拉斯矩阵和无符号拉普拉斯矩阵。多项式π(L(G); x)=per(xI-L(G))(或π(Q(G); x)=per(xI-Q(G)))称为G的拉普拉斯积和多项式(或无符号拉普拉斯积和多项式)。在本文中, 证明了两类双圈图是(无符号)拉普拉斯积和多项式确定的。

关键词: 积和式, (无符号)拉普拉斯矩阵, (无符号)拉普拉斯积和多项式, (无符号)拉普拉斯积和同谱

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

中图分类号: 

  • O157.6

图1

双圈图d(p, q, r)与θ(p, q, r)"

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