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Optimal open-locating-dominating sets in infinite triangular grids

2014/03/27 by Rex K. Kincaid, Kincaid, Rex, Allison Oldham +3
Computer Science · #Advanced Graph Theory Research #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #FOS: Mathematics #Optimization and Search Problems

paper · pdf · doi:10.48550/arxiv.1403.7061

openalex publication_date 2014/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An open-locating-dominating set (OLD-set) is a subset of vertices of a graph such that every vertex in the graph has at least one neighbor in the set and no two vertices in the graph have the same set of neighbors in the set. This is an analogue to the well-studied identifying code in the literature. In this paper, we prove that the optimal density of the OLD-set for the infinite triangular grid is 4/13.

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