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The \textit{square} of a graph $G$, denoted by $G^2$, is obtained from $G$ byadding an edge to connect every pair of vertices with a common neighbor in $G$.In this paper we prove that for every planar graph $G$ with maximum degree atmost $5$, $G^2$ admits a proper vertex coloring using at most $17$ colors,which improves the upper bound $18$ recently obtained by Hou, Jin, Miao, andZhao.

Square Coloring of Planar Graphs with Maximum Degree at Most Five