Estrada Index Of Bicyclic Graphs

In2000Estrada introduced an index to quantify the degree of folding of long chain polymeric molecules, which is called Estrada index later. Since then the Estrada index is extensively applied in molecular chemistry, quantum chemistry, information science and complex network etc.The trees (or with some prescribed structural property) with maximal Estrada index was characterized, and also the unicyclic graph with with maximal Estrada index was characterized. So, naturally the next problem is to characterize the bicyclic graph with maximal Estrada index. The main result of this thesis is to present some structural property of the bicyclic graph with maximal Estrada index, which will be useful for the characterization of the extreme graph.The thesis is organized as follows. In Chapter one some concepts and notations, together with background of Estrada index, are introduced. In Chapter two a survey of Estrada index is given. The last Chapter is our main work, that is, the structural property of the bicyclic graph with maximal Estrada index.