The dominating partition dimension and locating-chromatic number of graphs - Muhammad Ridwan; Hilda Assiyatun; Edy Tri Baskoro (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2023)
For every graph G, the dominating partition dimension of G is either the same as its partition dimension or one higher than its partition dimension. In this paper, we consider some general connections among these three graph parameters: partition dimension, locating-chromatic number, and dominating partition dimension. We will show that βp(G)≤ηp(G)≤χL(G) for any graph G with at least 3 vertices. Therefore, we will derive properties for which graphs G have ηp(G)=βp(G) or ηp(G)=βp(G)+1.