Several Topological Indices Of Non-trivial Quasi-tree Graphs

Topological index is an invariant used to describe some characteristics of molecular graph,and it is an important research topic in chemical graph theory,which is of great significance to the structure of chemical molecules.In this paper,we mainly research the extremal problem of non-trivial quasi-tree graphs of order n with respect to two kinds of topological exponents is discussed,and the corresponding polar graphs are characterized.In the first part of this paper,we introduce the origin of graph theory,as well as the basic concept used in the article,and introduce the research status of the quasi-tree.In the second part,we proved the upper and lower bounds of wiener index of non-trivial quasi-tree graphs of order n by the mathematical induction method,and characterized the corresponding extremal graphs.In the third part,we conclude the lower bound of the Sum-connectivity index of the non-trivial quasi-tree of order n by classification and discussion method,and characterized the extremal graphs.