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《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (7): 65-72.doi: 10.6040/j.issn.1671-9352.0.2020.230

• • 上一篇    

剖分Q-邻接冠图的广义特征多项式及其应用

杨影1,李沐春1*,张友2   

  1. 1.兰州交通大学数理学院, 甘肃 兰州 730070;2.商丘学院计算机工程学院, 河南 商丘 476000
  • 发布日期:2021-07-19
  • 作者简介:杨影(1995— ), 女, 硕士研究生, 研究方向为图论与组合优化. E-mail:17853480529@163.com*通信作者简介:李沐春(1964— ), 女, 硕士, 教授, 研究方向为图论与组合优化. E-mail:limuchunmath@163.com
  • 基金资助:
    国家自然科学基金资助项目(11961041);甘肃省自然科学基金资助项目(17JR5RA099);兰州交通大学青年基金资助项目(2017004)

Generalized characteristic polynomial of subdivision Q-neighbourhood corona graphs and its application

YANG Ying1, LI Mu-chun1*, ZHANG You2   

  1. 1. College of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China;
    2. College of Computer and Engineering, Shangqiu College, Shangqiu 476000, Henan, China
  • Published:2021-07-19

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摘要： 设正则图G1和G2的剖分Q-邻接点冠图G1□·QG2是由Q(G1)和|V(G1)|个点不交的G2的拷贝,通过连接V(G1)中第i 个顶点的所有邻点与第i个G2的拷贝的所有点后得到的图; 剖分Q-邻接边冠图G1□—〓QG2是由Q(G1)和|I(G1)|个点不交的G2的拷贝,通过连接 I(G1)中第 i个顶点的所有邻点与第i个G2的拷贝的所有点后得到的图。其中Q(G1)是由图G1的每条边上插入一个新点且当图G1的2条边相邻时对应的2个新点之间连接一条边后得到的图, I(G1)是图G1中每条边上插入的新点所构成的集合。分别确定了剖分Q-邻接点冠图G1□·QG2和剖分Q-邻接边冠图G1□—〓QG2 的广义特征多项式及其相应的Φ-谱。得到了G1□·QG2和G1□—〓QG2的规范拉普拉斯谱, 同时也构造了一些Φ-同谱无穷类。

关键词: 剖分Q-邻接点冠图, 剖分Q-邻接边冠图, 广义特征多项式, Φ-同谱图

Abstract: The subdivision Q-neighborhood vertex corona G1□·QG2 of two regular graphs G1 and G2 for regular is the graph obtained from vertex disjoint union of Q(G1) and |V(G1)| copies of G2, and by joining the neighbors of the ith vertex of |V(G1)| to every vertex in the ith copy of G2; the subdivision Q-neighborhood edge corona G1□— QG2 is the graph obtained from vertex disjoint union of Q(G1) and |I(G1)| copies of G2, and by joining the neighbors of the ith vertex of I(G1) to every vertex in the ith copy of G2, where Q(G1) is obtained from G1 by inserting a new vertex into every edge of G1 and then joining by edges those pair of new vertices which lie on adjacent edges of G1, and I(G1) is denoted by the set of such new vertices inserted in each edge of G1. Based on above, the generalized characteristic polynomial and Φ-spectrum of G1□·QG2 and G1□— QG2 are determined, respectively. As an application, their normalized Laplacian spectrum are obtained. Besides, infinitely many pairs of Φ-cospectral mates are also constructed.

Key words: subdivision Q-neighborhood vertex corona, subdivision Q-neighborhood edge corona, generalized characteristic polynomial, Φ-cospectral graphs

中图分类号: 

  • O157.5
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