Maximum values of the edge Mostar index in tricyclic graphs

For a graph $G$, the edge Mostar index of $G$ is the sum of $\mathrm{\mid }{m}_u(e\mathrm{\mid }G)-m_v(e\mathrm{\mid }G)\mathrm{\mid }$ over all edges $e=uv$ of $G$, where $m_u(e\mathrm{\mid }G)$ denotes the number of edges of $G$ that have a smaller distance in $G$ to $u$ than to $v$, and analogously for $m_v(e\mathrm{\mid }G)$. This paper mainly studies the problem of determining the graphs that maximize the edge Mostar index among tricyclic graphs. To be specific, we determine a sharp upper bound for the edge Mostar index on tricyclic graphs and identify the graphs that attain the bound.