路矩阵的谱及两类组合图的路谱  

Path matrices and spectra of two composite graphs

作　　者：卢鹏丽[1] 栾睿 郭育红 陈娅红 LU Pengli;LUAN Rui;GUO Yuhong;CHEN Yahong(School of Computer and Communication, Lanzhou University of Technology, Lanzhou 730050, China;School of Mathematics and Statistics, Hexi University, Zhangye 734034, China;Department of Mathematics, Lishui University, Lishui 323000, China)

机构地区：[1]兰州理工大学计算机与通信学院,甘肃兰州730050 [2]河西学院数学与统计学院,甘肃张掖734034 [3]丽水学院数学系,浙江丽水323000

出　　处：《哈尔滨工程大学学报》2022年第2期262-267,共6页Journal of Harbin Engineering University

基　　金：国家自然科学基金项目(11361033,11861045,62162040).

摘　　要：为了研究和完善图谱理论,更好地反应图的结构,本文依据矩阵论和代数知识,证明了任意图的路矩阵的谱半径的下界和路谱能量的上界;给出了k-连通且k-正则图的两类组合图的路谱;定义了路整谱图,得到了一类特殊路整谱图类,并给出了路谱能量。Spectral radius lower bounds and path spectrum energy upper bounds of arbitrary graph matrices were proven,based on matrix theory and algebra,to study and perfect graph theory to better reflect graph structure.The path spectra of two kinds of composite graphs of k-connected,k-regular,and path integral spectral graphs were defined,a special class of path integral spectral graphs,and path spectral energies were all determined.

关 键 词：路矩阵 路谱半径 路谱 路整谱图 路谱能量 联图 冠图 双圈图 

分 类 号：O157.5[理学—数学]