Topological Index Of Several Classes Of Graph Operations

Graph theory is a very active branch of mathematics in recent years,which closely relate to matrix theory,group theory,probability theory,topology.It has important applications in computer science,physics,chemistry,operations research,network the-ory and other areas.The molecular topological index is constructed from the molecular graph mapping refers to a collection of compounds to the set of real numbers,which has applications in physics,chemistry and network theory.There is some relation between topological index to some physical properties and some chemical properties.There are nearly a thousand kinds of topological indices are proposed after the Wiener index were proposed in 1947.The Wiener(Zagreb)index is one of the most important chemical topological index.There are some important problems on the topological index of graphs,such as:(1)find the graphs with extremal topological index among all some type graphs;(2)give the computational formula of the topological index of some graphs;(3)find some properties of the topological index on invariants of graph.In this paper we main study the computational formulas of the Zagreb index and Wiener index of some new graphs,which are obtained by some operations to three given graphs Gi,G2,G3.In first Chapter,we introduce the background,content and the main works of this paper.In second Chapter,we give the computational formulas of the Zagreb indices and Wiener index of subdivision double corona,Q-graph double corona,R-graph double corona and total double corona by analyzing graph structures.In last Chapter,we introduce the definition of graph F(G1,G2*G3),then we gave the computational formulas of Zagreb index and Wie,ner index of graph F(G1,G2*G3).