The Wiener, Szeged and Pi-indices of a Phenylazomethine Dendrimer

Let G be a simple graph with vertex set and edge set . The function which assigns to each pair of vertices in , the length of minimal path from to , is called the distance function between two vertices. The distance function between and edge and a vertex is where for and. , . The Wiener index of a graph is denoted by and is defined by .In general this kind of index is called a topological index, which is a distance based quantity assigned to a graph. This is an invariant of the graph in the sense that if a graph H is isomorphic to then . The Wiener index for the first time was introduced by H. Wiener in [11] and is related to chemical substances. The definition of the Wiener index in terms of distance between vertices of a graph for the first time was given by Hosoya in [6]. This index is extensively studied by various authors, and we may refer the reader to [5] and [1] in which a new method is found to calculate the Wiener index of a graph. Another index that will be investigated in this paper is the Szeged index, which is defined as follows: