The Study Of The Extremal Problems Of The Edge Revised Szeged Index Among All Tricyclic Graphs

Chemical graph theory is an important branch of graph theory.Its main function is to simulate the molecular structure diagram of some organic compounds into the gen-eral connected graph in graph theory,and further analyze and study the structure of these graphs by mathematical methods,so as to obtain some properties of these organic compounds.As one of the main research contents of chemical graph theory,topological index is the numerical value derived from the molecular structure diagram by determining rules.These values are graph invariants and usually reflect some properties of molecules.Topological index is a bridge between molecular structures and molecular properties.It is widely used in theoretical chemistry,applied chemistry,pharmacology and biology.Among them,edge Szeged index and edge revised Szeged index are two important topo-logical indexes in chemical graph theory.In 2010,Zhou and Cai gave the lower bound of edge Szeged index of unicyclic graphs.In 2011,Dong determined the maximum and minimum of edge revised Szeged index of unicyclic graphs with m edge.In 2016,Liu and Chen gave the upper bound of edge revised Szeged index of bicyclic graphs.In 2020,Yao obtained the maximum and minimum of the edge Szeged index of the bicyclic graph.The edge revised Szeged of bicyclic graph was also obtained by Liu.In this paper,the extremal problems of the edge Szeged index and edge revised Szeged index is studied.The main contents include:The upper bound of edge revised Szeged index of tricyclic graphs,the lower bound of edge revised Szeged index of tricyclic graphs and the lower bound of Szeged index of tricyclic graphs.There are five parts in this paper:In the first part,mainly introducing the research background and current situation of edge（revised）Szeged index and some basic concepts are involved.In the second part,The conclusion is that when m≥17,（?）.In the third part,The conclusion is that when m≥17,^Sz*_e（G）≥1/2m²+71/4m-45.In the fourth part,The conclusion is that when m≥13,Sz_eG≥6m-15.In the fifth part,It is the summary and the prospect of future work.