On Some Extremal Results and Bounds of Additively Weighted Edge Mostar Index

The additively weighted edge Mostar index is a topological index(TI) defined as an extension of the edge Mostar index. In this paper, we determine the extrema of the additively weighted edge Mostar index for trees. Additionally, we compute the lower bound and first four upper bounds of additively weighted edge Mostar index of unicyclic graphs and the upper bound for cacti with a fixed number of cycles. All the graphs attaining the bounds are characterized. We also propose two conjectures on additively weighted edge Mostar index of bicyclic graphs.