On the Complexity of Some Variations of Y -Dominating Functions on Graphs
نویسندگان
چکیده
Let Y be a subset of real numbers. A Y dominating function of a graph G = (V, E) is a function f : V → Y such that u∈NG[v] f(u) ≥ 1 for all vertices v ∈ V , where NG[v] = {v} ∪ {u|(u, v) ∈ E}. Let f(S) = u∈S f(u) for any subset S of V and let f(V ) be the weight of f . The Y -domination problem is to find a Y -dominating function of minimum weight for a graph. In this paper, we study the variations of Y domination such as {k}-domination, k-tuple domination, signed domination, and minus domination for some classes of graphs. We present a unified approach to these four domination problems on strongly chordal graphs. Notice that trees, block graphs, interval graphs, and directed path graphs are subclasses of strongly chordal graphs. This paper also gives complexity results for these four domination problems on doubly chordal graphs, dually chordal graphs, chordal bipartite graphs, and planar graphs.
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تاریخ انتشار 2006