Global Cototal Domination in Graphs - T. Nicholas; T. Sheeba Helen (International Journal of Mathematics And its Applications, 2018)
A set of vertices D in a graph G is a dominating set, if each vertex of G is dominated by some vertices of D. The domination number γ(G) is the minimum cardinality of a dominating set of G. A dominating set D of a graph G is a global dominating set if D is also a dominating set of G. The global domination number γ_g(G) is the minimum cardinality of a global dominating set of G. A dominating set D of a graph G is a cototal dominating set if the induced sub graph, V-D has no isolated vertices. The cototal domination number γ_cot(G) is the minimum cardinality of a cototal dominating set of G. In this paper we introduce a new concept, the global cototal domination number γ_gcot(G). A dominating set D of a graph G is a global cototal dominating set if D is both a global dominating set and a cototal dominating set. The global cototal domination number γ_gcot(G) is the minimum cardinality of a global cototal domination set of G. We initiate the study of global cototal domination number and present bounds and some exact values of γ_gcot(G) for some classes of graphs.