The Reciprocal Randiî’‚ Index Of Unicyclic Graphs And Wiener And Zagreb Indices Of Mycielskian Graphs

The study of topological indices of graphs is a very important part of graph theory.In general, a topological index, sometimes also known as a graph-theoretic index, is a numerical invariant of a graph. There are several topological indices have been de?ned such as, Wiener index W, hyper-Wiener index W W, PI index, Hosoya index, ABC index,Wiener polarity index Wp, Szeged index, the ?rst and second Zagreb index M1、M2, general Randi′c index Rα. Many of them have been applied as means for modeling chemical,pharmaceutical and other properties of molecules.The generalized Randi′c index Rαof a connected graph G =(V, E) is de?ned as Rα(G) =∑uv∈E(G)(dG(u)dG(V))α. Where α ∈ R is a real number. Hence,R-12 is the ordinary Randi′c index of G. When α =12, R 12 is called reciprocal Randi′c index,denoted RR(G).Mycielski introduced a new graph transforms a graph G into a new graph μ(G), which is called the M ycielskian of G. The generalized μm(G)(m ≥ 0) are the natural generalization of the M ycielskian graph. In this thesis, we characterize the unicyclic graph with the maximum RR index. Moreover, we present the formulae for the W iener type index, the ?rst Zagreb and the second Zagreb indexes of(generalized) M ycielskian of a connected graph.