单圈共轭图的最小广义Randic指标R-1

摘要

The general Randic index Rα=Rα (G) ors graph is the sum of the weights (d(u)d(v))α of all edges uv of G, where d(u) denotes the degree of the vertex u and α is an arbitrary real number. In this paper, a sharp lower bound on the R-1 for conjugated unicyclic graphs(i.e., unicyclic graphs with a perfect matching) is established and the corresponding extremal graphs are characterized. These graphs are also extremal over all the unicyclic conjugated chemical graphs.%图G的广义Randic指标定义为Rα=Rα(G)=∑uv∈E(G)(d(u)d(v))αrn,其中d(u)是G的顶点u的度,α是任意实数.本文确定了单圈共轭图的广义Randic指标R-1的严格下界,并刻划了达到最小R-1的极图,这类极图还是化学图.