单圈共轭图的最小广义Randi指标R_(-1)(英文)

On the unicyclic conjugated molecules with minimum general Randi index R_(-1)

图G的广义Randic指标定义为Rα=Rα（G）=∑uv∈E（G）（d（u）d（v））^α，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．

The general Randic index Rα = R,α （G） of a graph is the sun, 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 tmicyclic graphs（i.e., unicyelic graphs with a perfect, matching） is established and tile corresponding extremal graphs are characterized. These graphs are also extremal over all the unicyclic conjugated chemical graphs.