The dominating partition dimension and locating-chromatic number of graphs.

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 β_p(G)≤η_p(G)≤χL(G) for any graph G with at least 3 vertices. Therefore, we will derive properties for which graphs G have η_p(G)=β_p(G) or ηp(G)=β_p(G)+1. [ABSTRACT FROM AUTHOR]