论文标题
加入产品和局部抗原色的常规图
On join product and local antimagic chromatic number of regular 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 $承认当地的抗魔法标签，则图$ g $称为本地抗原。 biftion $ f：e \ to \ {1,2，\ ldots，q \} $称为$ g $的本地抗害怕标签，如果对任何两个相邻的顶点$ u $和$ v $，我们都有$ f^+（u）\ ne f^+（u）\ ne f^+（v） $ e（u）$是事件的一组$ u $。因此，如果为顶点$ v $分配了颜色$ f^+（v）$，则任何本地抗原标签都会引起$ g $的适当顶点着色。本地的抗原色编号，表示为$χ_{la}（g）$，是$ g $的本地抗原标签所取的最小诱导颜色数量。令$ g $和$ h $为两个顶点脱节图。 $ g $和$ h $（表示为$ g \ vee h $）的联接图是图$ v（g \ vee h）= v（g）\ cup v（h）$和$ e（g \ vee h）= e（g \ vee h）= e（g）\ cup e（h）在本文中，我们显示了具有任意较大级别，规律性和局部抗原色数的不完整常规图的存在。
Let $G = (V,E)$ be a connected simple graph of order $p$ and size $q$. A graph $G$ is called local antimagic if $G$ admits a local antimagic labeling. A bijection $f : E \to \{1,2,\ldots,q\}$ is called a local antimagic labeling of $G$ if for any two adjacent vertices $u$ and $v$, we have $f^+(u) \ne f^+(v)$, where $f^+(u) = \sum_{e\in E(u)} f(e)$, and $E(u)$ is the set of edges incident to $u$. Thus, any local antimagic labeling induces a proper vertex coloring of $G$ if vertex $v$ is assigned the color $f^+(v)$. The local antimagic chromatic number, denoted $χ_{la}(G)$, is the minimum number of induced colors taken over local antimagic labeling of $G$. Let $G$ and $H$ be two vertex disjoint graphs. The join graph of $G$ and $H$, denoted $G \vee H$, is the graph $V(G\vee H) = V(G) \cup V(H)$ and $E(G\vee H) = E(G) \cup E(H) \cup \{uv \,|\, u\in V(G), v \in V(H)\}$. In this paper, we show the existence of non-complete regular graphs with arbitrarily large order, regularity and local antimagic chromatic numbers.
