The Energy of a Graph: Old and New Results
The Energy of a Graph: Old and New Results
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DOI：
10.1007/978-3-642-59448-9_13
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
I. Gutman
中科院分区：
文献类型：
--
作者：
I. Gutman
设G是一个有n个顶点和n个中边的图。G的能量记为E = E（G），是G的特征值的绝对值之和。本文简述了E与一类有机分子总电子能量的关系。给出了E（G）与G的特征多项式之间的关系，E的上下界，特别是依赖于n和m个图的关于E的极值的上下界，E（G）>E（Kn）的n-顶点图.具有极大值E的n-顶点图的刻画是一个公开问题。
LetGbe a graph possessingnvertices andmedges. The energy ofG, denoted byE = E(G), is the sum of the absolute values of the eigenvalues ofG. The connection betweenEand the total electron energy of a class of organic molecules is briefly outlined. Some (known) fundamental mathematical results on E are presented: the relation betweenE(G)and the characteristic polynomial ofG, lower and upper bounds forE, especially those depending onnandm, graphs extremal with respect toE,n-vertex graphs for whichE(G)>E(Kn). The characterization of then-vertex graph(s) with maximal value ofEis an open problem.