Document Type

Article

Publication Date

3-17-2013

Publication Title

Graphs and Combinatorics

Abstract

Abstract. Given a graph G, the k-dominating graph of G, Dk(G), is defined to be the graph whose vertices correspond to the dominating sets of G that have cardinality at most k. Two vertices in Dk(G) are adjacent if and only if the corresponding dominating sets of G differ by either adding or deleting a single vertex. The graph Dk(G) aids in studying the reconfiguration problem for dominating sets. In particular, one dominating set can be reconfigured to another by a sequence of single vertex additions and deletions, such that the intermediate set of vertices at each step is a dominating set if and only if they are in the same connected component of Dk(G). In this paper we give conditions that ensure Dk(G) is connected.

Keywords

Domination, Reconfiguration problems, Chordal graphs, Bipartite graphs

Volume

30

Issue

3

First Page

609

Last Page

617

DOI

10.1007/s00373-013-1302-3

ISSN

1435-5914

Comments

Peer reviewed post-print.

The final publication is available at Springer via http://dx.doi.org/10.1007/s00373-013-1302-3

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