(Revised)Szeged Index Of Some Graphs

Chemical graph theory is an important subdivision of graph theory.It mainly sim-ulates the molecular structure diagrams of some organic compounds as the general con-nected graphs in graph theory,and further studies the structure of these simulated graphs by mathematical methods,so as to obtain some properties of these org anic compounds.Topological index is one of the main research contents of chemical graph theory.These values are derived from the determined rules in the molecular structure diagram.And these values are graph invariants,which usually reflect some properties of molecules.Topological index establishs a bridge between molecular structures and molecular proper-ties,which are widely used in theoretical chemistry,applied chemistry,pharmacology and biology research and etc.Szeged index and revised Szeged index are two important topo-logical indices in the study of chemical graph theory.In this paper,Szeged indices of some simple connected graphs are studied.The main contents include that the(revised)Szeged index of join graph and corona graph of two simple graphs,the relationship between the(revised)Szeged index of the double graph of G,a simple graph,and the(revised)Szeged index of G,the(revised)Szeged index of Mycielski graphs of some special graphs,the(revised)Szeged index of starlike tree and double starlike tree,and the(revised)Szeged indices of two kinds of Hexagonal Systems.This paper is divided into five chapters to discuss.In Chapter one,the background and basic concepts of(revised)Szeged index are given.In Chapter two,the(revised)Szeged index of the join graph and the corona graph of two simple graphs are determined.In Chapter three,the(revised)Szeged index of the double graph of a simple graph and the(revised)Szeged index of Mycielski graphs of some special graphs are given.In Chapter four,the(revised)Szeged index of starlike tree and double starlike tree are given,and the edge Szeged index is further obtained by the relationship between Szeged index and edge Szeged index.In Chapter five,the(revised)Szeged index of the hexacyclic system and Mobius hexacyclic system are determined.