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Packing in regular graphs


Michael A. Henning
William F. Klostermeyer

Abstract

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 p(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 p(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 p(G) ≥ n/(k2 − 1).

Mathematics Subject Classification (2010): 05C65.

Keywords: Packing, regular graphs, Moore graphs


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eISSN: 1727-933X
print ISSN: 1607-3606