2020/11/24 by Min Feng, Feng, Min, Kaishun Wang +3
Computer Science · Mathematics · #05C12 #05C20 #05C35 #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #math.CO #msc:05C12 #msc:05C20 #msc:05C35
paper · pdf · doi:10.48550/arxiv.2011.12038
openalex publication_date 2020/11/24 · arxiv created 2020/12/07 · arxiv updated 2020/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using the two way distance, we introduce the concepts of weak metric dimension of a strongly connected digraph Γ. We first establish lower and upper bounds for the number of arcs in Γ by using the diameter and weak metric dimension of Γ, and characterize all digraphs attaining the lower or upper bound. Then we study a digraph with weak metric dimension 1 and classify all vertex-transitive digraphs having weak metric dimension 1. Finally, all digraphs of order n with weak metric dimension n-1 or n-2 are determined.