Reza Sharafdini

Let G be a simple connected graph and H be the subgraph of G induced by the set of non-pendent vertices of G. In this case, H is called the kenogram of G. Let v be a pendent vertex of G connected to u. Then uv is a pendent edge of G not belonging to H. E(G) = E(H) ∪ E1(G), where E(H) and E1(G) denote the set of edges of H and the set of all pendent edges of G. The distance between the vertices u and v of G is the number of edges of a shortest path in G connecting them. The Wiener index of G is defined as the sum of distances between all vertices of G. In this thesis, we consider Wiener index and some of its extensions like Schultz, Szeged, Padmakar-Ivan, Gutman and variable Wiener index. In this thesis, we study the relationship between these indices of a simple connected graph and its kenogram.