论文标题
梯子图的优美着色
Graceful Coloring of Ladder Graphs
论文作者
论文摘要
非空图$ g =（v，e）$的优雅k颜色是一种适当的顶点着色$ f：v（g）\ rightarrow \ lbrace \ lbrace 1,2，...，k \ rbrace $，$ k \ geq 2 $，可诱导适当的边缘着色$ f^{*}：e（g）：e（g）： 。 。 ，k-1 \ rbrace $由$ f^{*}（uv）= | f（u）-f（v）| $，其中$ u，v \ in v（g）$。 $ g $具有优美$ k $颜色的最低$ k $称为优美的色度，$χ_{g}（g）$。本文研究了一些梯形图的优美色数。
A graceful k-coloring of a non-empty graph $G=(V,E)$ is a proper vertex coloring $f:V(G)\rightarrow\lbrace 1,2,...,k \rbrace$, $k\geq 2$, which induces a proper edge coloring $f^{*}:E(G)\rightarrow\lbrace 1, 2, . . . , k-1 \rbrace $ defined by $f^{*}(uv) = |f(u)-f(v)|$, where $u,v\in V(G)$. The minimum $k$ for which $G$ has a graceful $k$-coloring is called graceful chromatic number, $χ_{g}(G)$. The graceful chromatic number for a few variants of ladder graphs are investigated in this article.
