非毛虫树的最大能量与最小能量  

Maximal and Minimal Energies of Noncaterpillar

作　　者：张冰 ZHANG Bing(Guangdong Polytechnic Normal University,Guangzhou Guangdong 510665)

机构地区：[1]广东技术师范大学数学与系统科学学院,广东广州510665

出　　处：《广东技术师范大学学报》2021年第3期57-59,100,共4页Journal of Guangdong Polytechnic Normal University

摘　　要：设G为n个点的简单图,λ_(1),λ_(2),…,λ_(n)为图G的n个特征值,图G的能量定义为E(G)=|λ_(1)|+|λ_(2)|+…+|λ_(n)|.我们定义毛虫树为一棵去掉其所有的悬挂点后成仅为一条路的树.设R_(n)为所有的含有n个点的非毛虫树的集合.研究了R_(n)中图的能量,刻画了R_(n)中具有最大能量和最小能量的图.If G is a graph consisting of n nodes and λ_(1),λ_(2),…,λ_(n) are its eigenvalues,then the energy of G is defined as E(G)=|λ_(1)|+|λ_(2)|+…+|λ_(n)| Recall that a caterpillar is a tree in which removal of all pendant vertices gives a path.Let R_(n) be the set of all noncaterpillar trees with n vertices.In this paper,we determine the graphs in R_(n) with maximal and minimal energies in R_(n).

关 键 词：能量 特征值 非毛虫树 

分 类 号：O157[理学—数学]