On the difference between atom‐bond connectivity index and Randić index of binary and chemical trees

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 Randić ( 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.