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 relativeto ks;s. the graph g is k-supercritical relative to ks;s if t(g) = k and t(g + e) = k - 2 for alle 2 e(h). the 2002 paper by t.w. haynes, m.a. henning and l.c. van der merwe, total dominationsupercritical 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 tok2k+1;2k+1 of diameter 5, for each k  2. however, the families of graphs in their proof are not thecase. we present a correction of this theorem.