Graph–theoretic degree–based descriptors play a central role in chemoinformatics and QSPR/QSAR modelling, yet most classical indices either focus purely on vertex degrees or treat bond contributions in a purely multiplicative way. In this work we introduce and systematically study a new family of modified bond-based indices in which each edge \ (uv E (G) \) is weighted by a local bond factor \ (T (uv) = G (u) + G (v) -2\) in the denominator, coupled with a vertex kernel in the numerator. This construction yields modified versions of the first and second Zagreb indices, the Forgotten and Yemen indices, several connectivity-type descriptors (product, sum, Nirmala, ABC, CAB, GA, harmonic, and misbalance prodeg), as well as Sombor- and Dharwad-type bond indices. We first present a unified edge–partition representation for any symmetric kernel, expressing each modified index as a finite sum over degree classes \ (E (₀, ₁) (G) \). This framework allows us to derive closed-form expressions for all sixteen modified bond-based indices on a broad collection of benchmark families: paths \ (P₍\), cycles \ (C₍\), complete graphs \ (K₍\), complete bipartite graphs \ (K₌, ₍\), stars \ (S₍\), friendship graphs \ (F₍\), wheels \ (W₍\), book graphs \ (B₍\), Dutch windmill graphs \ (D₍^ (m) \), and hypercubes \ (Qd\). The resulting tables reveal clear asymptotic growth patterns and highlight which structures are extremal for the modified descriptors. Moreover, we obtain sharp degree–extreme bounds for a representative subset of the indices in terms of the order \ (n\), size m, and the minimum and maximum degrees \ (\) and \ (\), with equality characterizing regular graphs. The proposed modified bond-based indices thus provide a flexible and analytically tractable family of descriptors that couple vertex and bond information in a novel way, and are well suited as structured features for modern chemoinformatics and graph-based machine-learning models on molecular graphs. Finally, to demonstrate predictive utility in a hypothesis-driven setting, we further benchmark these \ (^mBI\) descriptors within a large multi-task QSAR/QSPR pipeline on 3, 219 ChEMBL antibacterial molecules across ten continuous properties using a heterogeneous model zoo under three descriptor scenarios, where the combined descriptors scenario achieves the best overall generalisation (Macro Test \ (R² = 0. 861\) ; Global zRMSE \ (= 0. 373\) ), improving upon the Physicochemical descriptors scenario (Macro Test \ (R² = 0. 852\) ; Global zRMSE \ (= 0. 385\) ).
Altairi et al. (Sat,) studied this question.