论文标题
邻居产品区分了亚地铁图的电晕总颜色
Neighbor product distinguishing total colorings of corona of subcubic graphs
论文作者
论文摘要
适当的$ [k] $ - 图$ g $的总颜色$ c $是$ v（g）\ bigcup e（g）$ c $ c $（g）$ to $ [k] = \ {1,2，\ cdots，k \} $，以便$ c（x）$ c（x）\ neq c（y）$ x $，$ x $ y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y v（g）或$ y $事件。令$ \ prod（v）$表示$ c（v）$的产品，以及带有$ v $的所有边缘事件的颜色。对于e（g）$中的每个边缘$ uv \，如果$ \ prod（u）\ neq \ prod（v）$，则颜色$ c $称为邻居产品，区分$ g $的总颜色。我们使用$花$χ” _ {\ prod}（g \ circ h）\leqΔ（g \ circ h）+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 $c(x)\neq c(y)$ for which $x$, $y\in V(G)\bigcup E(G)$ and $x$ is adjacent 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 $G$. we use $χ"_{\prod}(G)$ to denote the minimal value of $k$ in such a coloring of $G$. In 2015, Li et al. conjectured that $Δ(G)+3$ colors enable a graph to have a neighbor product distinguishing total coloring. In this paper, we consider the neighbor product distinguishing total coloring of corona product $G\circ H$, and obtain that $χ"_{\prod}(G\circ H)\leq Δ(G\circ H)+3$.
