Packing Coloring of Some Undirected and Oriented Coronae Graphs

Abstract

The packing chromatic number χρ(G) of a graph G is the smallest integer k such that its set of vertices V(G) can be partitioned into k disjoint subsets V1, . . . , Vk, in such a way that every two distinct vertices in Vi are at distance greater than i in G for every i, 1 ≤ i ≤ k. For a given integer p ≥ 1, the p-corona of a graph G is the graph obtained from G by adding p degree-one neighbors to every vertex of G. In this paper, we determine the packing chromatic number of p-coronae of paths and cycles for every p ≥ 1.

Keywords

• packing coloring
• packing chromatic number
• corona graph
• path
• cycle
• 05c15
• 05c70
• 05c05