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Erd\\H{o}s and Ne\\v{s}et\\v{r}il conjectured in 1985 that the upper bound of $\\chi_{s}'(G)$ is $\\frac{5}{4}\\Delta^{2}$ when $\\Delta$ is even and $\\frac{1}{4}(5\\Delta^{2}-2\\Delta +1)$ when $\\Delta$ is odd, where $\\Delta$ is the maximum degree of $G$. The conjecture is proved right when $\\Delta\\leq3$. 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We denote the strong chromatic index by $\\chi_{s}'(G)$ which is the minimum number of colors that allow a strong edge-coloring of $G$. Erd\\H{o}s and Ne\\v{s}et\\v{r}il conjectured in 1985 that the upper bound of $\\chi_{s}'(G)$ is $\\frac{5}{4}\\Delta^{2}$ when $\\Delta$ is even and $\\frac{1}{4}(5\\Delta^{2}-2\\Delta +1)$ when $\\Delta$ is odd, where $\\Delta$ is the maximum degree of $G$. The conjecture is proved right when $\\Delta\\leq3$. 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