Packing colorings of the corona product of the path Pn and the cycle Cn with an edge K₂

Abstract

Given a graph G and a positive integer i, an i-packing in G is a subset X of V (G) such that the distance dG(u, v) between any two distinct vertices u, v ∈ X is greater than i. The packing chromatic number χρ(G) of a graph G is the smallest integer k such that the vertex set of G can be partitioned into sets Vi, i ∈ [k], where each Vi is an i-packing. In this paper, we determine the packing chromatic number of the Corona products of paths and cycles of small order (at most 11 vertices) with an edge and obtain bounds for the packing chromatic number of corona products of paths and cycles of larger order with an edge.