Progress on Self Identifying Codes
Abstract
The concept of an identifying code for a graph was introduced by Karpovsky, Chakrabarty, and Levitin in 1998 as the problem of covering the vertices of a graph such that we can uniquely identify any vertex in the graph by examining the vertices that cover it. An application of an identifying code would be to detect a faulty processor in a multiprocessor system. In 2020, a variation of identify code called "self-identifying code" was introduced by Junnila and Laihonen, which simplifies the task of locating the malfunctioning processor. In this paper, we continue to explore self-identifying codes. In particular, we prove the problem of determining the minimum cardinality of a self-identifying code for an arbitrary graph is NP-complete and we investigate minimum-sized self-identifying code in several classes of graphs, including cubic graphs and infinite grids.
Keywords
Cite
@article{arxiv.2504.14124,
title = {Progress on Self Identifying Codes},
author = {Devin Jean and Suk Seo},
journal= {arXiv preprint arXiv:2504.14124},
year = {2025}
}