On identifying codes on oriented graphs
Soura Sena Das, Sagnik Sen
Abstract
This article studies identifying codes in oriented graphs from a computational complexity perspective. We investigate the F-Id Code problem, where given a simple graph G and a vertex subset C, which induces a subgraph in the family 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 Fd of d-regular graphs, we establish a complete dichotomy by proving that the problem is polynomial-time solvable for d≤1 and NP-complete for all d≥2.
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