PI Index Of Unicyclic Graphs, Bicyclic Graphs And Line Graphs Of Tree

The PI index is one of the important fields of graph theory. The study of the PI index not only has important theoretical value, but also have a wide range of applications in the fields of chemistry, physics, complex networks. Therefore,it greatly promoted the study of PI index properties of Graphs.There are two chapters in this paper. The details are as follows:In chapter 1, we introduce the background of the PI index theory and some notations, and recall the related corona operation issues of current research progress.In chapter 2, we give a simple and direct method to determine PI index formulae of unicyclic graphs, bicyclic graphs and line graphs of tree. Moreover, we give sharp lower and upper bound on the PI index of unicyclic graphs, bicyclic graphs and line graphs of tree and characterize the case of equality for bounds.