2011/11/15 by Juan A. Rodriguez-Velazquez, Juan A. Rodríguez‐Velázquez, Rodriguez-Velazquez, Juan A. +4
Computer Science · Engineering · Mathematics · #05C05 #05C12 #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #graph theory and CDMA systems #math.CO #msc:05C05 #msc:05C12
paper · pdf · doi:10.48550/arxiv.1111.3513
openalex publication_date 2011/11/15 · arxiv created 2013/05/02 · arxiv updated 2013/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given an ordered partition Π=\P1,P2, ...,Pt\ of the vertex set V of a connected graph G=(V,E), the partition representation of a vertex v∈ V with respect to the partition Π is the vector r(v|Π)=(d(v,P1),d(v,P2),...,d(v,Pt)), where d(v,Pi) represents the distance between the vertex v and the set Pi. A partition Π of V is a resolving partition if different vertices of G have different partition representations, i.e., for every pair of vertices u,v∈ V, r(u|Π)≠ r(v|Π). The partition dimension of G is the minimum number of sets in any resolving partition for G. In this paper we obtain several tight bounds on the partition dimension of unicyclic graphs.