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Let $\\prod(v)$ denote the product of $c(v)$ and the colors on all the edges incident with $v$. For each edge $uv\\in E(G)$, if $\\prod(u)\\neq \\prod(v)$, then the coloring $c$ is called a neighbor product distinguishing total coloring of $G$. we use $\\chi\"_{\\prod}(G)$ to denote the minimal value of $k$ in such a coloring of $G$. 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Let $\\prod(v)$ denote the product of $c(v)$ and the colors on all the edges incident with $v$. For each edge $uv\\in E(G)$, if $\\prod(u)\\neq \\prod(v)$, then the coloring $c$ is called a neighbor product distinguishing total coloring of $G$. we use $\\chi\"_{\\prod}(G)$ to denote the minimal value of $k$ in such a coloring of $G$. 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