Linear model based on neighborhood ABS index for graph energy in benzenoid hydrocarbons and maximum index cactus...

The atom-bond-sum (ABS) connectivity index, developed by integrating the degree information from the atom-bond and sum connectivity indices, has attracted significant attention for its effectiveness in correlating thermodynamic properties of chemical structures. We study the ABS index by capturing the neighborhood degree information of atoms and its relationship to the π-electron energy in a dataset of alternant benzenoid hydrocarbons, revealing a strong correlation of 0.999. Moreover, graphs with the maximum index generally correspond to molecules with high stability or desired reactivity. Therefore, we aim to identify and describe the unique cactus graph that achieves the maximum neighborhood ABS index for a fixed number of cycles and pendent vertices, providing insights into structural features and highlighting the significance of the neighborhood ABS index in molecular chemistry.