Small Randié Index Ordering of Trees with \(k\) Pendant Vertices

Abstract

The Randić index of an organic molecule whose molecular graph is \(G\) is the sum of the weights \((d(u)d(v))^{1/2}\) of all edges \(uv\) of \(G\), where \(d(u)\) denotes the degree of the vertex \(u\) of the molecular graph \(G\). Among all trees with \(n\) vertices and \(k\) pendant vertices, the extremal trees with the minimum, the second minimum, and the third minimum Randić index were characterized by Hansen, Li, and Wu \(et al\)., respectively. In this paper, we further investigate some small Randić index properties and give other elements of small Randić index ordering of trees with \(k\) pendant vertices.