on a conjecture on edge mostar index of bicyclic graphs

For an edge e = uv of a graph g, mu(e|g) denotes the number of edges closerto the vertex u than to v (similarly mv(e|g)). the edge mostar index moe(g), of a graphg is defined as the sum of absolute differences between mu(e|g) and mv(e|g) over alledges e = uv of g. h. liu et al. proposed a conjecture on extremal bicyclic graphs withrespect to the edge mostar index [1]. even though the conjecture was true in case of thelower bound and proved in [2], it was wrong for the upper bound. in this paper, wedisprove the conjecture proposed by h. liu et al. [1], propose its correct version andprove it. we also give an alternate proof for the lower bound of the edge mostar indexfor bicyclic graphs with a given number of vertices.