论文标题
直径的锤子图3
Radio number of Hamming graphs of diameter 3
论文作者
论文摘要
对于$ g $，简单，连接的图，一个顶点标签$ f：v（g）\ rightarrow \ mathbb {z} _ + $称为$ \ textit {ndinder for（v）| f（f（u） - $ u，v \ in V（g）$。 $ g $的$ \ textit {无线电编号} $是$ g $的所有无线电标签的最小跨度。如果存在$ \ {1,2，...，| v（g）| \} $上的bijective无线电标签，$ g $称为$ \ textit {无线电优雅图} $。我们确定所有直径的无线电编号$ 3 $ hamming图，并表明它们的无限子集是广播优美的。
For $G$ a simple, connected graph, a vertex labeling $f:V(G)\rightarrow \mathbb{Z}_+$ is called a $\textit{radio labeling of}$ $G$ if it satisfies $|f(u)-f(v)|\geq \operatorname{diam}(G) + 1 - d(u,v)$ for all distinct vertices $u,v\in V(G)$. The $\textit{radio number}$ of $G$ is the minimal span over all radio labelings of $G$. If a bijective radio labeling onto $\{1,2,...,|V(G)|\}$ exists, $G$ is called a $\textit{radio graceful graph}$. We determine the radio number of all diameter $3$ Hamming graphs and show that an infinite subset of them is radio graceful.
