[PDF][PDF] Total domination critical graphs with respect to relative complements
TW Haynes, MA Henning, LC Van der Merwe - Ars Comb., 2002 - combinatorialpress.com
A set S of vertices of a graph G is a total dominating set if every vertex of V (G) is adjacent to
some vertex in S. The total domination number ye (G) is the minimum cardinality of a total
dominating set of G. Let G be a spanning subgraph of K, and let H be the com-plement of G
relative to K,; that is, K.,,= GGH is a factorization of K.,,. The graph G is ke-critical relative to
K., if y (G)= k and y (G+ e)< k for all ee E (H). We study ke-critical graphs rela-tive to K., for
small values of k. In particular, we characterize the 3e-critical and 4e-critical graphs.
some vertex in S. The total domination number ye (G) is the minimum cardinality of a total
dominating set of G. Let G be a spanning subgraph of K, and let H be the com-plement of G
relative to K,; that is, K.,,= GGH is a factorization of K.,,. The graph G is ke-critical relative to
K., if y (G)= k and y (G+ e)< k for all ee E (H). We study ke-critical graphs rela-tive to K., for
small values of k. In particular, we characterize the 3e-critical and 4e-critical graphs.
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