Some Results On Graph Parameters Based On Distance And Matching Energy

In 1947,the chemist Harold Wiener proposed the concept of Wiener index in order to estimate the hydrocarbons boiling point,defined as W(G)=?{u,v}(?)V(G)dG(u,v).By the calculation,we found the value solved by this method is very close to the real boiling point.Since Schultz index and modified Schultz index are closely related to Wiener index and widely used in chemistry,more and more scholars are devoted to this field.In the second chapter,we study the Wiener index of unicyclic graphs,and obtain Schultz index and modified Schultz index of a graph with given girth and their relationship.Formal expressions for Wiener index,Schultz index and modified Schultz index of the unicyclic graph are presented,including the relationship between them.In the third chapter,we give the Wiener index of rectangular grid network system by means of recursive method.As a corollary,we also give a square lattice network Wiener index of the system.Matching energy of a graph was introduced by Gutman and Wagner in 2012,which can be defined as the sum of absolute values of zeros of its matching polynomial.In the last chapter,we characterize extremal graphs with respect to their matching energy.