科研之友
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摘要
We initiate the study of double outer-independent domination in graphs. A vertex of a graph is said to dominate itself and all of its neighbors. A double outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D, and the set V(G)\D is independent. The double outer-independent domination number of a graph G is the minimum cardinality of a double outer-independent dominating set of G. First we discuss the basic properties of double outer-independent domination in graphs. We find the double outer independent domination numbers for several classes of graphs. Next we prove lower and upper bounds on the double 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 Nordhaus-Gaddum type inequalities.
- 出版日期2017-7
