Levenshtein图：可分解性、自同构与决定集
Levenshtein Graphs: Resolvability, Automorphisms & Determining Sets
摘要：
我们引入Levenshtein图的概念，类似于Hamming图，但使用编辑距离而不是Hamming距离;特别是，Levenshtein图允许不同长度的底层字符串（节点）。我们刻画了这些图的各种性质，包括它们的测地距离与编辑距离相同的充分必要条件，它们的自同构群和决定数，以及它们的度量维数的上界。对于后者，我们构造了一个解析集组成的两个运行字符串和一个算法，该算法计算的编辑距离之间的字符串长度$k$和任何单运行或两个运行字符串在$O(k)$操作。
英文摘要：
We introduce the notion of Levenshtein graphs, an analog to Hamming graphs but using the edit distance instead of the Hamming distance; in particular, Levenshtein graphs allow for underlying strings (nodes) of different lengths. We characterize various properties of these graphs, including a necessary and sufficient condition for their geodesic distance to be identical to the edit distance, their automorphism group and determining number, and an upper bound on their metric dimension. Regarding the latter, we construct a resolving set composed of two-run strings and an algorithm that computes the edit distance between a string of length $k$ and any single-run or two-run string in $O(k)$ operations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
