Neighbor product distinguishing total colorings of corona of subcubic graphs

A proper $[k]$-total coloring $c$ of a graph $G$ is a mapping $c$from $V(G)\bigcup E(G)$ to $[k]=\{1,2,\cdots,k\}$ such that$c(x)\neq c(y)$ for which $x$, $y\in V(G)\bigcup E(G)$ and $x$ isadjacent to or incident with $y$. Let $\prod(v)$ denote theproduct of $c(v)$ and the colors on all the edges incident with$v$. For each edge $uv\in E(G)$, if $\prod(u)\neq \prod(v)$, thenthe coloring $c$ is called a neighbor product distinguishing totalcoloring of $G$. By $\chi''_{\prod}(G)$, we denote the minimalvalue of $k$ in such a coloring of $G$. In this paper, weconsidered the corona graph $G$ of two arbitrary subcubic graphsand confirmed that $\chi''_{\prod}(G)\leq\Delta(G)+3$.