单圈图的增强型Zagreb指数的下界

Lower Bounds of Augmented Zagreb Index of Unicyclic Graphs

设图G=(V, E)是具有n(n≥3)个顶点、m条边的简单连通图,图G的度序列为{d1,d2,...,dn},定义图G的增强型Zagreb指数(记作AZI)为:AZI=AZI(G)=∑ij∈E(didj/di=dj-2)^3.利用有关不等式的性质,讨论了单圈图的增强型Zagreb指数,得到了该类图的增强型Zagreb指数的几个精确下界.

Let G=(V, E) be a simple connected graph with n(n≥3) vertices and m edges, with vertex degree sequence {d1,d2,...,dn}. The augmented Zagreb index of graphs G is defined as AZI,AZI=AZI(G)=∑ij∈E(didj/di=dj-2)^3. Using the properties of several inequalities, the AZI of unicyclic graphs is investigated, and some new sharp lower bounds for AZI are obtained.