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Bezegov$\\acute{a}$ et al. conjectured that $\\chi_{st}^{'} (G )\\leq \\lfloor\\frac{3\\Delta}{2}\\rfloor+1$ when $G$ is an outerplanar graph with\n  maximum degree $\\Delta \\geq 3.$ In this paper we obtained that $\\chi_{st}^{'}(G) \\leq \\Delta+6$ when $G$ is an 2-connected outerplanar graph with diameter 2 or 3. 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The it star chromatic index, $\\chi_{st}^{'} (G ),$ of $G$ is the minimum number $k$ for which $G$ has a star edge coloring by $k$ colors. In \\cite{LB},\n  L. Bezegov$\\acute{a}$ et al. conjectured that $\\chi_{st}^{'} (G )\\leq \\lfloor\\frac{3\\Delta}{2}\\rfloor+1$ when $G$ is an outerplanar graph with\n  maximum degree $\\Delta \\geq 3.$ In this paper we obtained that $\\chi_{st}^{'}(G) \\leq \\Delta+6$ when $G$ is an 2-connected outerplanar graph with diameter 2 or 3. 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