单圈分子图的第一广义Zagreb指标的极值

Extreme Values of Unicyclic Molecular Graph on the First General Zagreb Index

第一广义Zagreb指标定义为0Rα(G)=∑i∈V(G)d(i)α,其中d(i)为i顶点的度,α为除0和1之外的所有实数。单圈分子图是指最大度不超过4且边数等于顶点数的简单连通图。本文通过一个引理,给出了单圈分子图的第一广义Zagreb指标达到极值的必要条件。

The First General Zagreb index can be defined as, as is the degree of the vertex i, and is a real number except for 0 and 1. The unicyclic molecular graph refers to the degree not exceeding 4 and its edge equals to the simple connected graph. The essay worked out the first general Zagreb index＇s necessary condition to attain extreme value in single molecular graph.