The Research Of Merriifeld-simmons Ndex And Hosoya Index In Some Graphs

In this paper, based on the previous study of the index in chemical graphswe determined the extremal graphs of bicyclic graphs with k pendant verticesof the maximum Merrifield Simmons index and bicyclic graphs with kpendant vertices of the smallest Hosoya index and Hosoya index in tricyclicgraphs.The thesis is arranged as follows:Section one is devoted to the introduction of some basic concepts andsymbols in chemical graph theory, simply reviewed the development history,current studies and some problems waiting for solving in the field of extremalgraphs of Merrifield Simmons index and some related result of Hosoyaindex in chemical graphs.In Section Two, we study the extremal graph about the maximum MerrifieldSimmons index and the smallest Hosoya index of Bicyclic graphs with k pen-dant vertices.In Section Three, we study the smallest Hosoya index of in tricyclic graphs.