International Journal of Wiener Index of Some Graphs in the Context of Switching Operation

Abstract. A topological representation of a molecule is called molecular graph. A molecular graph is a collection of points representing the atoms in the molecule and set of lines representing the covalent bonds. These points are named vertices and the lines are named edges in graph theory language. One of the most widely known topological descriptors is Wiener index. It is named after chemist Harold Wiener who introduced in the year 1947. The Wiener index W (G) is a distance-based topological invariant much used in the study of the structure-property and the structure-activity relationships of various classes of biochemically interesting compounds. It is defined by the sum of the distances between all (ordered) pairs of vertices of G. In this paper, we find the Wiener index of switching the consecutive vertices in a cycle, path graphs