Two Topological Indices Based On The Zagreb Indices

Two oldest and well-known graph invariants are Zagreb indices (M1 and M2) first introduced in 1972[6,8], where Gutman and Trinajstic examined the dependence of total π-electron energy on molecular structure. The Randic (R) index is introduced for the effect of molecular branching[36]. In the past 30 years, these topological indices have been the classical indices in the chemical-mathematician mind. For the sake of development, recently, Gutman propose some new topological indices based on these traditional indices. We use the traditional method to study these new topological indices, then get some beautiful results.The thesis is arranged as follows:In the first chapter, we introduce the definition and the background of the Reduced Reciprocal Randic index and Reduced Second Zagreb index, give the basic notations and terminology related to this thesis.In the second chapter, we study maximum values of Reduced Second Zagreb index in the unicycle graphs, and attained the maximum and the minimum values of the Reduced Second Zagreb index in the unicycle graphs of all n-vertex graphs.In the three chapter, Reduced Reciprocal Randic index of tree graphs, we have achieved the extremal graphs (with a fixed number of vertices) with greatest RRR in-dices, then proved that the Gutman’s conjecture is ture.