In this paper we look at the problem of adjacency labeling of graphs. Given a family of undirected graphs the problem is to determine an encoding-decoding scheme for each member of the family such that we can decode the adjacency information of any pair of vertices only from their encoded labels. Further, we want the length of each label to be short (logarithmic in $n$, the number of vertices) and the encoding-decoding scheme to be computationally efficient. We proposed a simple tree-decomposition based encoding scheme and used it give an adjacency labeling of size $O(k \log k \log n)$-bits. Here $k$ is the clique-width of the graph family. We also extend the result to a certain family of $k$-probe graphs.

翻译：在本文中,我们查看图表的相近标签问题。 鉴于一组无方向的图表, 问题在于确定每个家庭成员的编码解码方案, 这样我们就能将任何一对脊椎的对应信息从他们的编码标签中解码出来。 此外, 我们希望每个标签的长度短( 以美元计的对数, 脊椎数) 和编码解码方案能够高效地计算。 我们提出了一个基于树解码的简单编码方案, 并使用它来给 $O( k\log k\log n) 位元的大小提供对应标签 。 这里$k$是图形家族的圆边线 。 我们还将结果扩展至某个以 $k$- probe 图表为主的家族 。