Abstract
A dominating set in a graph G is a connected dominating set of G if it induces a connected subgraph of G. The minimum number of vertices in a connected dominating set of G is called the connected domination number of G, and is denoted by γ c (G). Let G be a spanning subgraph of K s,s and let H be the complement of G relative to K s,s ; that is, K s,s = G ⊕ H is a factorization of K s,s . The graph G is k-γ c -critical relative to K s,s if γ c (G) = k and γ c (G + e) < k for each edge e ∈ E(H). First, we discuss some classes of graphs whether they are γ c -critical relative to K s,s . Then we study k-γ c -critical graphs relative to K s,s for small values of k. In particular, we characterize the 3-γ c -critical and 4-γ c -critical graphs.
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Chen, Xg., Sun, L. Connected domination critical graphs with respect to relative complements. Czech Math J 56, 417–423 (2006). https://doi.org/10.1007/s10587-006-0027-3
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DOI: https://doi.org/10.1007/s10587-006-0027-3