Abstract
Topological indices are graph invariants computed by the distance or degree of vertices of the molecular graph. In chemical graph theory, topological indices have been successfully used in describing the structures and predicting certain physicochemical properties of chemical compounds. The Randic index is one of the classical graph-based molecular structure descriptors that has found countless applications in chemistry and pharmacology. The mathematical background of this index is also well elaborated.
The Randic index of a graph G is defined as
R(G) = Sigma(uv is an element of E(G)) 1/root deg(u)deg(v),
where E(G) is the set of edges and deg(u), deg(v) are the degrees of the vertices u and v, respectively. In this research, we introduce the entire Randic index of graph. Exact values of this index for some graph families are obtained and some important properties of this new index are established.