Packing chromatic numbers of finite super subdivisions of graphs

Abstract

The packing chromatic number of a graph G, denoted by χ_{ρ}(G), is the smallest integer k such that the vertex set of G can be partitioned into sets V_{i}, i∈{1,…,k}, where each V_{i} is an i-packing. In this paper, we present some general properties of packing chromatic numbers of finite super subdivisions of graphs. We determine the packing chromatic numbers of the finite super subdivisions of complete graphs, cycles and neighborhood corona graphs of a cycle and a path respectively of a complete graph and a path.

Keywords: Packing chromatic number, packing coloring, neighborhood corona, finite super subdivision.