Tricyclic Graph with Minimum Randić Index

Abstract

The Randić index of a graph G is the sum of (dG(u)dG(v))−12 over all edges uv of G, where dG(u) denotes the degree of vertex u in G. In this paper, we investigate a few graph transformations that decrease the Randić index of a graph. By applying those transformations, we determine the minimum Randić index on tricyclic graphs and characterize the corresponding extremal graphs.