SEMIGLOBAL TOTAL DOMINATION IN GRAPHS

T. Nicholas; T. Sheeba Helen

T. Nicholas Department of Mathematics, St. Judes College,Thoothoor, TamilNadu, India
T. Sheeba Helen Department of Mathematics, Holy Cross College (Autonomous), Nagercoil -4, TamilNadu, India

Keywords: Semicomplete graph, global total domination number, semicomplementary graph, semiglobal total domination number.

Abstract

A subset D of vertices of a connected graph G is called a semiglobal total dominating set if D is a dominating set for G and G^scand < D > has no isolated vertex in G, where G^sc is the semi complementary graph of G. The semiglobal total domination number is the minimum cardinality of a semiglobal total dominating set of G and is denoted by γ_sgt(G). In this paper exact values for γ_sgt(G) are obtained for some graphs like cycles, wheel and paths are presented as well.

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