Sum-connectivity Index Of Tricyclic Graphs

Graph theory is a branch of mathematics, graph can represent many meanings, Therefore, graph theory has many important application in many aspects. In recent years graph theory is combined with the many application disciplines and the formation of branches. For example, Algebraic graph theory、topological graph theory、chemical graph theory、random graph、graph algorithm. The molecular topological index is one of the most active research fields in modern chemical graph theory.Since H.Wiener raised the first molecular topological index, Wiener index in1975, hundreds of molecular topological index including the Sum-connectivity index has been widely researched and application.This paper mainly studies the Sum-connectivity index in chemical graph theory and find out the corresponding extreme graphs, The full text is divided into three chapters, the specific structure is as follows:In chapter Ⅰ, We mainly introduce the research background of the Sum-connectivity index and the basic knowledge of graph theory which will be used in the article and introduce and prove that4important transformations and5lemmas.In Chapter Ⅱ, We introduce some research results about the Sum-connectivity index and focusing on the largest sum-connectivity index of tree, unicyclic graph and bicyclic graph, we derive the maximum Sum-connectivity index of unicyclic graphs, bicyclic graph used the above lemma again and find out corresponding extreme graphs.In Chapter Ⅲ, We use the lemma of1.2,1.3,1.4,1.5to derive the maximum Sum-connectivity index of tricyclic graphs containing only three cycle and finding out the corresponding extreme graphs.