Abstract
This article is devoted to establishing some extremal results with respect to the difference of two well-known bond incident degree indices [atom-bond connectivity (ABC) index and Randic (R) index] for the chemical graphs representing alkanes. More precisely, the first three extremal trees with respect to ABC - R are characterized among all n-vertex binary trees (the trees with maximum degree at most 3). The n-vertex chemical trees (the trees with maximum degree at most 4) having the first three maximum ABC - R values are also determined.