Split Total Domination Number of Some Special Graphs
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Keywords:
Split Dominating Set, Total Dominating Set, Split Total Dominating SetAbstract
A dominating set for a graph $G = (V,E)$ 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 $\gamma(G)$ is the number of vertices in a smallest dominating set for G. In this paper a new parameter, Split Total Dominating Set $S$ and the Split Total Domination Number $\gamma_{st} (G)$ has been introduced. A dominating set is called split total dominating set if $\langle V-D\rangle$ is disconnected and every vertex $v \in V$ is adjacent to an element of D. The split total domination number is given by $\gamma_{st} (G)$. 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.
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