论文标题
连续的锤子图的无线电标记
Consecutive Radio Labeling of Hamming Graphs
论文作者
论文摘要
对于图$ g $，$ g $的$ k $ -radio标签是$ g $的顶点的正整数分配，因此图表上越近两个顶点，标签的差异越大。具体来说，$ \ vert f（u）-f（v）\ vert \ geq k + 1 -d（u，v）$，其中$ f（u）$是$ g $ in vertex $ u $的标签。在这里，我们考虑$ g $是完整图的笛卡尔产品时的情况。具体而言，我们希望找到使用连续整数并确定何时可能的最佳标签。我们建立了Amanda Niedzialomski的一张纸，并构建了一个框架，用于发现连续的锤子图广播标签，从最小的未知图（$ k_3^4 $）开始，为此我们使用我们的构造提供了最佳标签。
For a graph $G$, a $k$-radio labeling of $G$ is the assignment of positive integers to the vertices of $G$ such that the closer two vertices are on the graph, the greater the difference in labels is required to be. Specifically, $\vert f(u)-f(v)\vert\geq k + 1 - d(u,v)$ where $f(u)$ is the label on a vertex $u$ in $G$. Here, we consider the case when $G$ is the Cartesian products of complete graphs. Specifically we wish to find optimal labelings that use consecutive integers and determine when this is possible. We build off of a paper by Amanda Niedzialomski and construct a framework for discovering consecutive radio labelings for Hamming Graphs, starting with the smallest unknown graph, $K_3^4$, for which we provide an optimal labeling using our construction.
