【作者】 王红专；

【导师】 邓汉元；

【作者基本信息】 湖南师范大学 ， 基础数学， 2006， 硕士

【摘要】 设G=(V,E)是一个简单连通图,V和E分别为G的顶点集和边集。那么,G的广义拓扑指数有四种 其中d_v表示G中顶点v的度,m≥2是正整数。G的广义拓扑指数是G的0-阶Randi(?)指数和Zagreb指数的推广。 本文我们研究单圈图的广义拓扑指数,利用图的变换,刻划了具有最大,次大,第三大和最小,次小,第三小广义拓扑指数的单圈图的特征。更多还原

【Abstract】 Let G — (V, E) be a simple and connected graph with the vertex set V and the edge set E. The four generalized topological indices for G are defined as the followingwhere d_v is the degree of vertex v and m ≥ 2 is an integer. The four topological indices of G are generalized from the zeroth-order Randic index:and the first zagreb index:In this paper, we investigate the four generalized topological indices through the method of graph transformations. All unicycle graphs with the first three largest values and the first three smallest values of the four generalized topological indices are characterized.更多还原