Atom-bond Connectivity Index

In this paper, based on the previous study of the topological index of graphs, we further research atom-bond connectivity index, we study the maximum values of atom-bond connectivity index in the class of tricyclic graphs, we have the first and second maximum values of the atom-bond connectivity index in the class of tricyclic graphs of all n-tricyclic graphs; And we also research atom-bond connectivity index of Eulerian graphs, we have Eulerian graphs (with a fixed number of vertices) with smallest and greatest ABC indices.The thesis is arranged as follows:In the first chapter, we introduce the definition and the background of the Atom-bond Connectivity index, give the basic notations and terminology related to this thesis, and and current studies. The succeeding two chapters are the main contributions of this thesis:In the second chapter, we study maximum values of atom-bond connectivity index in the class of tricyclic graphs, and attained the first and second maximum values of the atom-bond connectivity index in the class of tricyclic graphs of all n-tricyclic graphs.In the three chapter, atom-bond connectivity index of Eulerian graphs, we have Eulerian graphs (with a fixed number of vertices) with smallest and greatest ABC indices.