Inverse degree, randić index and harmonic index of graphs

Abstract

Let G be a graph with vertex set V and edge set E. Let di be the degree of the vertex vi of G. The inverse degree, Randić index, and harmonic index of G are defined as ID =Σvi∈V 1/di, R =Σvivj∈E 1/√di dj, and H = Σvivj∈E 2/(di + dj ), respectively. We obtain relations between ID and R as well as between ID and H. Moreover, we prove that in the case of trees, ID > R and ID > H.