Disproof of a conjecture on the edge Mostar index

For a given connected graph $G$, the edge Mostar index $M{o}_e(G)$ is defined as $M{o}_e(G)={\sum }_{e=uv\in E(G)}\mathrm{\mid }{m}_u(e\mathrm{\mid }G)-m_v(e\mathrm{\mid }G)\mathrm{\mid }$, where $m_u(e\mathrm{\mid }G)$ and $m_v(e\mathrm{\mid }G)$ are respectively, the number of edges of $G$ lying closer to vertex $u$ than to vertex $v$ and the number of edges of $G$ lying closer to vertex $v$ than to vertex $u$. We determine a sharp upper bound for the edge Mostar index on bicyclic graphs and identify the graphs that attain the bound, which disproves a conjecture proposed by Liu et al. [Iranian J. Math. Chem. 11(2) (2020) 95–106].