可重图的Randi指标的极值问题

Multigraphs with Extremal Randi Indices

图G的Randi指数,χ(G),是分子图的一种拓扑指标,它的值可以反映分子的许多物理化学性质.在化学分子中双键是普遍存在的.为此,研究了恰有一条重边的可重图的Randi指标的极值问题,给出了树图及化学树图的Randi指标的极值及相应的结构.

X（G）, the Randic index of G, is a proposed molecular descriptor, and is well correlated with a variety of physico-chemical properties of alkanes. Since multiple bonds are often encountered in molecular graph in chemistry. The purpose of this paper is to derive the extreme values of Randic index for molecular graph with exactly one multi- ple bond. The definitions of 1-multitree and chemical 1-multitree are given. Then the extreme values of Randic index for 1-multitree and chemical 1-multitree are obtained, respectively. And the corresponding structures are also dis- cussed.