论文标题
关于融合图的局部抗原总标记
On local antimagic total labeling of amalgamation graphs
论文作者
论文摘要
令$ g =（v，e）$为连接的简单订单$ p $和size $ q $的图形。如果$ g $承认当地的抗原（总）标签，则图$ g $称为本地抗原（总）。 bifact $ g：e \ to \ {1,2，\ ldots，q \} $称为$ g $ $ g $的本地抗害怕标签，如果对任何两个相邻的顶点$ u $和$ v $，我们都有$ g^+（u）\ ne g^+（u）\ ne g^+（v） $ e（u）$是事件的一组$ u $。同样，一个两次培养$ f：v（g）\ cup e（g）\ to \ {1,2，\ ldots，p +q \} $被称为本地抗原总标签$ g $的$ g $，如果任何两个相邻的顶点$ u $和$ v $，我们有$ w_f（u） \ sum_ {e \ in E（u）} f（e）$。因此，如果为color $ g^+（v）$（分别为$ w_f（u）$），则任何本地抗原（总）标签都会诱导$ g $的正确顶点着色，为$ g $。局部抗原（总）色度，表示为$χ_{la}（g）$（分别$χ_{LAT}（g）$）是$ g $的本地抗原（总）标签上采取的诱导颜色的最低诱导颜色数量。在本文中，我们确定了$χ_{LAT}（g）$，其中$ g $是完整图的合并。
Let $G = (V,E)$ be a connected simple graph of order $p$ and size $q$. A graph $G$ is called local antimagic (total) if $G$ admits a local antimagic (total) labeling. A bijection $g : E \to \{1,2,\ldots,q\}$ is called a local antimagic labeling of $G$ if for any two adjacent vertices $u$ and $v$, we have $g^+(u) \ne g^+(v)$, where $g^+(u) = \sum_{e\in E(u)} g(e)$, and $E(u)$ is the set of edges incident to $u$. Similarly, a bijection $f:V(G)\cup E(G)\to \{1,2,\ldots,p+q\}$ is called a local antimagic total labeling of $G$ if for any two adjacent vertices $u$ and $v$, we have $w_f(u)\ne w_f(v)$, where $w_f(u) = f(u) + \sum_{e\in E(u)} f(e)$. Thus, any local antimagic (total) labeling induces a proper vertex coloring of $G$ if vertex $v$ is assigned the color $g^+(v)$ (respectively, $w_f(u)$). The local antimagic (total) chromatic number, denoted $χ_{la}(G)$ (respectively $χ_{lat}(G)$), is the minimum number of induced colors taken over local antimagic (total) labeling of $G$. In this paper, we determined $χ_{lat}(G)$ where $G$ is the amalgamation of complete graphs.
