Packing in regular graphs

Document Type

Article

Publication Date

7-4-2018

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 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).

Publication Title

Quaestiones Mathematicae

Volume

41

Issue

5

First Page

693

Last Page

706

Digital Object Identifier (DOI)

10.2989/16073606.2017.1398193

ISSN

16073606

E-ISSN

1727933X

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