Like Degree Wiener Index for Molecular Graphs

A graph representing the molecular structure of a chemical compound is called a molecular graph. A molecular graph is a collection of points representing the atoms in the molecule and set of lines representing the covalent bonds. The physicochemical and biochemical properties of compounds depend strongly on their molecular structures. The construction and investigation of topological indices that could be used to describe molecular structures is one of the important directions of mathematical chemistry. The Wiener index of a graph is defined as the sum of distances between all pairs of vertices in a connected graph. Wiener index correlates well with many physicochemical properties of organic compounds and as such has been well studied over the last quarter of a century. In this paper we introduce a wiener type index called Like Degree Wiener index and study the same for few graph structures.