A set $C$ of vertices in a graph $G=(V,E)$ is an identifying code if it is dominating and any two vertices of $V$ are dominated by distinct sets of codewords. This paper presents a survey of Iiro Honkala's contributions to the study of identifying codes with respect to several aspects: complexity of computing an identifying code, combinatorics in binary Hamming spaces, infinite grids, relationships between identifying codes and usual parameters in graphs, structural properties of graphs admitting identifying codes, and number of optimal identifying codes.
翻译:图$G=(V,E)$中的顶点子集$C$称为识别码,若其既是支配集,且$V$中任意两个顶点被不同的码字集所支配。本文综述了Iiro Honkala在识别码研究中的多方面贡献,包括:识别码计算复杂性、二元汉明空间中的组合学、无限网格图、识别码与图论中常规参数的关系、允许识别码存在的图的结构性质,以及最优识别码的数量。