Packing Chromatic Number of Certain Dendrimers

Abstract

Abstract:The packing chromatic number χρ(G) of a graph G is the smallest integer k for which there exists a mapping f : V (G) −→ {1, 2, ..., k} such that any two vertices of color i are at distance at least i + 1. In bio-chemistry, dendrimers are synthetically produced monodisperse polymeric nanostructures with a tree-like, highly branched architecture. Applications of dendrimers typically involve conjugating other chemical species to the dendrimer surface that can function as detecting agents , affinity ligands, targeting components, radioligands, imaging agents, or pharmaceutically active compounds. In this paper, the packing chromatic number of certain dendrimers D 2,k , k = 1, 2, 3, 4 are calculated. We also post some open problems.