Given a graph G, the k-dominating graph of G, Dkβ(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 Dkβ(G) are adjacent if and only if
the corresponding dominating sets of G differ by either adding or deleting a
single vertex. The graph Dkβ(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 Dkβ(G). In this paper we give
conditions that ensure Dkβ(G) is connected.Comment: 2 figure, The final publication is available at
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