A NOTE ON THE TOTAL DOMINATION SUPERCRITICAL GRAPHS

Abstract. Let G be a connected spanning subgraph of Ks;s and let H be the complement of G relative to Ks;s. The graph G is k-supercritical relative to Ks;s if t(G) = k and t(G + e) = k - 2 for all e 2 E(H). The 2002 paper by T.W. Haynes, M.A. Henning and L.C. van der Merwe, \Total domination supercritical graphs with respect to relative complements" that appeared in Discrete Mathematics, 258 (2002), 361-371, presents a theorem (Theorem 11) to produce (2k + 2)-supercritical graphs relative to K2k+1;2k+1 of diameter 5, for each k  2. However, the families of graphs in their proof are not the case. We present a correction of this theorem.