some inequalities with respect to the difference between atom-bondconnectivity index and randi´c index

Let g be a simple and connected graph with vertex set v (g) and edge set e(g). the atom-bondconnectivity and randi´c index of graph g are two well-defined topological indices in chemical graphtheory. recently, ali and du [on the difference between atom-bond connectivity index and randi´c indexof binary and chemical trees, int. j. quantum chem. (2017) e25446] characterized some extremal resultswith the respect to the difference between atom-bond connectivity index and randi´c index for n-vertexbinary and chemical trees. in this paper, we establish some inequalities with respect to the differencebetween atom-bond connectivity index and randi´c index and study the relation between them.