调和指标的极值图  

The Extremal Graphs for Harmonic Index

作　　者：王晓[1] 汪小黎[1] 

机构地区：[1]商洛学院数学与计算机应用学院,陕西商洛726000

出　　处：《商洛学院学报》2015年第4期3-4,24,共3页Journal of Shangluo University

基　　金：商洛学院科研基金项目(12SKY011)

摘　　要：图G的调和指标定义为H(G)=Σuv∈E(G)2/d(u)+d(v),其中d(u)表示G中顶点u的度。给出图的调和指标的另一种表述形式,证明了所有同阶的非空正则图的调和指标都相等,并且是同阶数图的调和指标的上界;利用一个引理,证明了固定团数和独立集阶数的Split图的调和指标的下界,并给出相应的极图。The harmonic index of graph G is defined as H（G）=Σuv∈E（G）2/d（u）＋d（v）,where d（u） denotes the degree of vertex u in G. Another representation of harmonic index is given, it is proved that the harmonic index of nonempty regular graphs with the same order is equal, and the harmonic index of nonempty regular graphs is upper bound of graphs with fixed order. Using a lemma, the lower bound on harmonic index of Split graphs with fixed clique number and cardinality of independent set is given, the corresponding extremal graph is obtained.

关 键 词：调和指标 极值图 Split图 

分 类 号：O157.5[理学—数学]