图的一个运算及其在阶能量图上的应用  

A graph operation and its applications in orderenergetic graphs

作　　者：陈锦松[1] 杨书若月 刘剑萍 CHEN Jinsong;YANG Shuruoyue;LIU Jianping(School of Mathematics and Statistics,Fuzhou University,Fuzhou,Fujian 350108,China)

机构地区：[1]福州大学数学与统计学院,福建福州350108

出　　处：《福州大学学报（自然科学版）》2024年第6期635-638,共4页Journal of Fuzhou University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(12171089)。

摘　　要：图G的能量E(G)定义为G的邻接矩阵的所有特征值的绝对值之和.一个n阶图如果它的能量等于n,则称为阶能量图.结合图与矩阵的运算,特别是矩阵的Kronecker积,给出图的一个新的运算.进一步确定相应新图的谱;并应用该运算由给定的某些非阶能量图,构造出一系列新的阶能量图族;还由任意阶能量图,构造出3类新的阶能量图族.The energy E(G)of a graph G is defined as the absolute sum of the eigenvalues of its adjacency matrix.A graph G of order n is called an orderenergetic graph if E(G)=n.In this paper,we introduce a new graph operation by combining the graph and the matrix calculation,especially the Kronecker product of matrices.Furthermore,we obtain the adjacency spectrum of the result graph.And we construct infinite families of new orderenergetic graphs from a non-orderenergetic graph.Also,we generate three new classes of orderenergetic graphs from any orderenergetic graph.

关 键 词：阶能量图 能量 图的运算 KRONECKER积 

分 类 号：O157.5[理学—数学]