【摘要】 设G=(V,E)是一个图,其中顶点集V={v1,v2,…,vn}.G的Randic指数X(G)=∑vivjE1d(vi)d(vj),d(v)表示顶点v的度,Randic′指数是化学图论中常见的一个拓扑指数.通过计算,证明了六边形系统中完全冷凝苯类的Randic指数是其转向六边形个数和分枝六边形个数的单调递增函数,并给出了满足极值条件的两类六边形系统的结构.更多还原

【Abstract】 Let G=(V,E) be a graph,where V={v 1,v 2,...,v n} .The Randic ′ index of G is X(G)=∑v iv jE1d(v i)d(v j) ,where d(v) denotes the degree of the vertex v. Randic index is one of ordinary topological indices considered in chemical graph theory. Using counting arguments we show that the Randic index is monotone increasing over the number of turned hexagons and the number of branched hexagons,and two extremal hexagonal systems with respect to Randic ′ index are given.更多还原