Year: 2026
Type: preprint
Abstract: This article studies identifying codes in oriented graphs from a computational complexity perspective. We investigate the $\mathcal{F}$-Id Code problem, where given a simple graph $G$ and a vertex subset $C$, which induces a subgraph in the family $\mathcal{F}$, as inputs and ask whether it is possible to orient $G$ in such a way that $C$ becomes its oriented identifying code. Focusing on the family $\mathcal{F}_d$ of $d$-regular graphs, we establish a complete dichotomy by proving that the problem is polynomial-time solvable for $d\leq1$ and NP-complete for all $d\geq2$.
Source: arXiv (Cornell University)
Authors: Das, Soura Sena, Sen, Sagnik
Institution: Indian Institute of Technology Dharwad
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204556701
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