E-viri
Recenzirano
-
Henning, Michael A.; Klostermeyer, William F.
Quaestiones mathematicae, 07/2018, Letnik: 41, Številka: 5Journal Article
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/(k 2 − 1).
