您的位置：山东大学 -> 科技期刊社 -> 《山东大学学报（理学版）》

《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

PDF (PC)

204

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
[1] WANG W, LI F, LU H L, et al. Graphs determined by their generalized characteristic polynomials[J]. Linear Algebra and Its Applications, 2011, 434(5):1378-1387.
[2] FRUCHT R, HARARY F. On the corona of two graphs[J]. Aequationes Mathematicae, 1970, 4(3):322-325.
[3] BARIK S, PATI S, SARMA B K. The spectrum of the corona of two graphs[J]. SIAM Journal on Discrete Mathematics, 2007, 21(1):47-56
[4] HOU Y, SHIU W C. The spectrum of the edge corona of two graphs[J]. The Electronic Journal of Linear Algebra, 2010, 20(1):586-594.
[5] WANG S L, ZHOU B. The signless Laplacian spectra of the corona and edge corona of two graphs[J]. Linear and Multilinear Algebra, 2013, 61(2):197-204.
[6] LIU X G, ZHANG Z H. Spectra of subdivision-vertex join and subdivision-edge join of two graphs[J]. Bulletin of the Malaysian Mathematical Sciences Society, 2019, 42(1):15-31.
[7] SONG Caixia, HUANG Qiongxiang, HUANG Xueyi. Spectra of subdivision vertex-edge corona for graphs[J]. Adcances in Mathematics(CHINA), 2016, 45(1):37-47.
[8] LI Muchun, ZHANG You, WEN Fei. The normalized Laplacian spectrum of subdivision vertex-edge corona for graphs[J]. Journal of Mathematical Research with Applications, 2019, 39(3):221-232.
[9] WEN F, ZHANG Y, LI M C. Spectra of subdivision vertex-edge join of three graphs[J]. Mathematics, 2019, 7(2):171.
[10] DAS A, PANIGRAHI P. Normalized Laplacian spectrum of some Q-coronas of two regular graphs[J]. Discussiones Mathematicae-General Algebra and Applications, 2021, 41(1):127.
[11] CVETKOVIC D, ROWLINSON P, SIMIC S. Characterizations by spectra[M] //An Introduction to the Theory of Graph Spectra. Cambridge: Cambridge University Press, 2009: 104-135.
[12] HORN R A, ZHANG F Z. Basic properties of the schur complement[M] //The Schur Complement and Its Applications. New York: Springer-Verlag, 2005.
[13] HORN R A, JOHNSON C R. Topics in matrix analysis[M]. Cambridge: Cambridge University Press, 1994.
[1] 解承玲, 马海成. 两个点并路的匹配等价图类[J]. 《山东大学学报(理学版)》, 2021, 56(1): 29-34.
[2] 魏宗田,方慧,李银奎. 基于网络选址的设施系统可靠性[J]. 《山东大学学报(理学版)》, 2020, 55(10): 77-82.
[3] 李晶晶,边红,于海征. 亚苯基链的修正互惠度距离指标[J]. 《山东大学学报(理学版)》, 2020, 55(10): 71-76.
[4] 刘佳,孙磊. 不含4-圈或弦6-圈的平面图是(3,0,0)-可染的[J]. 《山东大学学报(理学版)》, 2018, 53(12): 31-40.
[5] 包丽娅,陈祥恩,王治文. 完全二部图K10,n(10≤n≤90)的点可区别E-全染色[J]. 《山东大学学报(理学版)》, 2018, 53(12): 23-30.
[6] 张友,黄丽娜,李沐春. 一类六角系统的点可区别边染色[J]. 《山东大学学报(理学版)》, 2018, 53(12): 41-47.
[7] 陈洪玲,王慧娟,高红伟. 可嵌入到欧拉示性数非负的曲面图的线性荫度[J]. 《山东大学学报(理学版)》, 2018, 53(12): 17-22.
[8] 李美莲,邓青英. 平图的transition多项式的Maple计算[J]. 山东大学学报（理学版）, 2018, 53(10): 27-34.
[9] 刘小花,马海成. Q形图的匹配能序及Hosoya指标排序[J]. 山东大学学报（理学版）, 2018, 53(8): 61-65.
[10] 寇艳芳,陈祥恩,王治文. K1,3,p和 K1,4,p的点可区别的IE-全染色及一般全染色[J]. 山东大学学报（理学版）, 2018, 53(8): 53-60.
[11] 陈宏宇,张丽. 4-圈不共点的平面图的线性2-荫度[J]. 山东大学学报（理学版）, 2017, 52(12): 36-41.
[12] 何玉萍,王治文,陈祥恩. mC8的点可区别全染色[J]. 山东大学学报（理学版）, 2017, 52(10): 24-30.
[13] 李亭亭,劳会学. 一类混合型数论函数的均值估计[J]. 山东大学学报（理学版）, 2017, 52(8): 70-74.
[14] 王晓丽,王慧娟,刘彬. 最大度为7的平面图全染色[J]. 山东大学学报（理学版）, 2017, 52(8): 100-106.
[15] 王晔,孙磊. 不含3圈和4圈的1-平面图是5-可染的[J]. 山东大学学报（理学版）, 2017, 52(4): 34-39.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 2018 《山东大学学报(理学版)》编辑部　
地址: 山东省济南市山大南路27号山东大学中心校区（250100）　电话: +86-0531-88366917　E-mail: xblxb@sdu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发