The dominating partition dimension and locating-chromatic number of graphs

Muhammad Ridwan, Hilda Assiyatun, Edy Tri Baskoro


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.


partition dimension, coloring, resolving, dominating, locating-chromatic

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