Total outer-independent domination in graphs
نویسنده
چکیده
We initiate the study of total outer-independent domination in graphs. A total outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D, and the set V (G) \ D is independent. The total outer-independent domination number of a graph G is the minimum cardinality of a total outer-independent dominating set of G. First we discuss the basic properties of total outerindependent domination in graphs. We find the total outer-independent domination numbers for several classes of graphs. Next we prove lower and upper bounds on the total outer-independent domination number of a graph, and we characterize the extremal graphs. Then we study the influence of removing or adding vertices and edges. We also give NordhausGaddum type inequalities.
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