In this paper, we considered the corona graph $G$ of two arbitrary subcubic graphs and confirmed that $\chi''_{\prod}(G)\leq\Delta(G)+3$.
📌 3 Maddede Bu Makale
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Amaç & Hipotez: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$c(x)\neq c(y)$ where $x$, $y\in V(G)\bigcup E(G)$ and $x$ isadjacent to or incident with $y$.
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Temel Bulgular & Veri:Let $\prod(v)$ denote the product of $c(v)$ and the colors on all the edges incident with $v$.
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Sonuç & Katkı:In this paper, we considered the corona graph $G$ of two arbitrary subcubic graphs and confirmed that $\chi''_{\prod}(G)\leq\Delta(G)+3$.
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$c(x)\neq c(y)$ where $x$, $y\in V(G)\bigcup E(G)$ and $x$ isadjacent to or incident with $y$. 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 $G$. By $\chi''_{\prod}(G)$, we denote the minimalvalue of $k$ in such a coloring of $G$. In this paper, we considered the corona graph $G$ of two arbitrary subcubic graphs and confirmed that $\chi''_{\prod}(G)\leq\Delta(G)+3$.
Dong, A., Zhang, W., Xue, B. (2026). Neighbor product distinguishing total colorings of corona of subcubic graphs. Hacettepe Journal of Mathematics and Statistics, Volume: 55 Issue: 4. https://doi.org/10.15672/hujms.1764088
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