The atom-bond sum-connectivity index and Randić index are two well-known topological indices in chemical graph theory. The difference between ABS index and Randić index for a graph \(\mathbb {G}\) is defined as \(ABS(\mathbb {G})-R(\mathbb {G})=\sum \limits _{\alpha \beta \in E(\mathbb {G})} \dfrac{(d_\alpha d_\beta (d_\alpha +d_\beta -2))^{\frac{1}{2}}-(d_\alpha +d_\beta )^{\frac{1}{2}}}{(d_\alpha d_\beta (d_\alpha +d_\beta ))^{\frac{1}{2}}},\) where \(d_\alpha \) is the degree of the vertex \(\alpha \in V(\mathbb {G}).\) We characterize the maximum of \(ABS-R\) for the class of bipartite graphs and chemical graphs with order n. In addition, the maximum tree of \(ABS-R\) with fixed diameter is explored. Moreover, \(ABS-R\) is observed to correlate well with the boiling point and molar refraction for some useful chemicals.
