链状四角系统及六角系统的GA指数

Geometric-Arithmetic Index of the Chain Polyomino Systems and Hexagonal Systems

设G=(V,E)是一个图,G的Geometric-Arithmetic指数(简称GA指数)在某些化学物品的物理性质方面具有良好的预测作用.通过计算,给出了直链、锯齿链四角系统和转向细胞个数为1的链状四角系统的GA指数公式;证明了六角系统中完全冷凝苯类的GA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.

Let G= （V, E） be a graph, The Geometric-Arithmetic index （called GA index） serves as a good predictor in the physical properties of certain chemicals.Using counting arguments , we can get the GA index of linear chain polyomino systems, zigzag chain polyomino systems, and chain polyomino systems with the number of turned cell being one. And we prove that the GA index is monotone increasing over the number of turned hexagons and the number of branched hexagons in hexagonal systems.