Packing in regular graphs
A set S of vertices in a graph G is a packing if the vertices in S are pairwise at distance at least 3 apart in G. The packing number of G, denoted by ρ(G), is the maximum cardinality of a packing in G. Favaron [Discrete Math. 158 (1996), 287–293] showed that if G is a connected cubic graph of order n different from the Petersen graph, then ρ(G) ≥ n/8. In this paper, we generalize Favaron’s result. We show that for k ≥ 3, if G is a connected k-regular graph of order n that is not a diameter-2 Moore graph, then ρ(G) ≥ n/(k2 − 1).
Digital Object Identifier (DOI)
Henning, & Klostermeyer, W. F. (2018). Packing in regular graphs. Quaestiones Mathematicae, 41(5), 693–706. https://doi.org/10.2989/16073606.2017.1398193