On The Research Of The Topological Index Of A Kind Of Plan Network

There is many of complex networks in the realistic society, some properties of complex networks is determined by its topological structure and topological index especially important for study the its topological structure. For a graph G(V, E), Randi? index is defines as follows: ???Evvji ji R 1)(dd G. Atom-bond connectivity index is defined as follows: ?????Evv jiji jidddd GABC211)(, where jivv denotes an edge and id denotes the degree of the vertex iv of G. This paper mainly discusses ABC index and Randi? index of the two-tree networks.The arrangements of the thesis are as follows:In chapter 1, we briefly introduce the background of complex networks and enumerate some results of the topological indices related to two-tree networks.In chapter 2, we mainly study the ABC index and Randi? index of a two-tree network and give an upper bound of the ABC index and bounds of Randi? index of a two-tree G with n vertices. We also determine the two-tree with the maximum and the second maximum ABC index. For Randi? index, we determine the two-tree with the maximum and the minimum Randi? index.In chapter 3, we give an upper bound of the ABC index of a generalized plane two-tree.We summarize and discuss some problems in the future in last chapter.