SPLIT TOTAL DOMINATION NUMBER OF SOME SPECIAL GRAPHS

Abstract

A dominating set for a graph is a subset D of V such that every vertex not in D is adjacent to at least one member of D. The domination number is the number of vertices in a smallest dominating set for G. In this paper a new parameter, Split Total Dominating Set and the Split Total Domination Number has been introduced. A dominating set is called split total dominating set if is disconnected and every vertex is adjacent to an element of D. The split total domination number is given by In this paper the split total domination number for some standard graphs like star, path, cycle, complete, ladder, wheel, bistar, tadpole, comb, barbell, butterfly and fan graphs are found. Also the complement of graphs are obtained.