| In this paper, based on the previous study of the index in chemical graphs we further research Merrifield—Simmons index in bicyclic graphs and tricyclic graphs and deter-mined the maximal to the seventh-maximal extremal graphs of Merrifield-Simmons indices in bicyclic graphs and researched the extremal graphs of that index of tricyclic graphs. We also do some research on find the methods of the smallest Merrifield—Simmons index in some classes of characteristics graphs, this greatly reduces the complexity of the process of research.The thesis is arranged as follows:Section One is devoted to the introduction of some basic concepts and symbols in chemical graph theory, simply reviewed the development history, current studies and some problems waiting for solving in the field of Hosoya index and Merrifield—Simmons index.In Section Two, we study the extremal graph and the value of bicyclic graphs, and determine the maximal to the seventh-maximal extremal graphs of Merrifield-Simmons indices in bicyclic graphs. The results are as follows:In Section Three, we study the smallest value of bicyclic graphs. Firstly, we research the smallest Merrifield-Simmons indices in four classes of tricyclic graphs i.e and Secondly, we determine the smallest Merrifield-Simmons index in those indices. In the course of the study, we use the special transforms to fast decrease the classes of graphs, and then reduce the complexity of the research process. The results are as follows:... |
