Further Properties of Trees with Minimal Atom-Bond Connectivity Index

Abstract EN

Let G = ( V , E ) be a graph the atom-bond connectivity (ABC) index is defined as the sum of weights ( ( d u + d v - 2 ) / d u d v ) 1 / 2 over all edges u v of G , where d u denotes the degree of a vertex u of G .

In this paper, we determined a few structural features of the trees with minimal ABC index also we characterized the trees with d i a [ T ] = 2 and minimal ABC index, where [ T ] is induced by the vertices of degree greater than 2 in T and d i a [ T ] is the diameter of [ T ] .