The k-Dominating Graph

Authors

Ruth Haas, Smith CollegeFollow
Karen Seyffarth, University of Calgary

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, D_k(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 D_k(G) are adjacent if and only if the corresponding dominating sets of G differ by either adding or deleting a single vertex. The graph D_k(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 D_k(G). In this paper we give conditions that ensure D_k(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 accepted manuscript.

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

Recommended Citation

Haas, Ruth and Seyffarth, Karen, "The k-Dominating Graph" (2013). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/3