Study On Topological Indices Of Graphs

Let G=(V,E)be a connected simple graph,where V(G)is the vertex set and E(G)is the edge set.We use d(v)to denote the degree of v.For each edge e=uv ∈E(G),we assign values to edges e with f(d(u),d(v)),and then we calculate the sum of values on all edges of graph G,which is called the f topological index of graph G,that is (?)The topological indexs studied in this thesis are Augmented Zagreb Index(AZI index)and Inverse Sum Indeg Index(I SI index),which are defined as (?)(?)The topological index of graph is an important parameter in chemical graph theory,and the extreme value problem of graph topological index is a class of important problems in chemical graph theory.The solution of the stable structure of many real compounds can be transformed into the extreme value problem of topological index of graphs.The main research results of this thesis are as follows.1.We determine the tree with maximum AZI index among trees with given diameter.We prove the upper bound of graphs with maximum AZI index among uni cycle graphs and unicycle graphs with given circle length,respectively.2.We determine the tree with maximum I SI index among chemical trees.We determine the tree with minimum ISI index among cactus and trees with given diameter,respectively.We determine the first to eleven trees ordered according to their ISI index.