the oriented arc coloring of generalized theta graphs

‎a homomorphism from $overrightarrow{g}$ to $overrightarrow{h}$ is a mapping $c$ from $v (overrightarrow{g})$ to $v (overrightarrow{h})$‎ ‎that preserves the arcs (that is $overrightarrow{c(u)c(v)} in a(overrightarrow{h})$ whenever $overrightarrow{uv} in a(overrightarrow{g})$)‎. ‎the oriented chromatic number of $overrightarrow{g}$ is the minimum order of an oriented graph $overrightarrow{h}$‎ ‎such that $overrightarrow{g}$ has a homomorphism to $overrightarrow{h}$‎. ‎the oriented arc chromatic number of $overrightarrow{g}$ is the minimum order of an oriented graph $overrightarrow{h}$‎ such that the line oriented graph‎ ‎of $overrightarrow{g}$ has a homomorphism to $overrightarrow{h}$‎. ‎in this paper‎, ‎we prove that oriented arc chromatic number‎ ‎of any oriented generalized theta graph lies between $1$ and $5$ and that these bounds are tight‎. ‎to do this‎, we obtain a homomorphism from the oriented generalized theta graph to tournament $t_5$‎.