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$C$若满足支配性且$V$中任意两个顶点由不同的码字集合支配,则称$C$为识别码。本文从以下多个方面综述了Iiro Honkala在识别码研究中的贡献:识别码的计算复杂度、二进制汉明空间中的组合数学、无限网格、识别码与图常见参数之间的关系、允许识别码的图的结构性质,以及最优识别码的数量。