In a graph G = (V, E), a subset S C V is a double dominating set if every vertex in V is dominated at least twice. The minimum cardinality of a double dominating set of G is the double domination number. A graph G is double domination edge critical if for any edge uv G E(G), the double domination number of G + uv is less than the double domination number of G. We investigate double " domination edge critical graphs and characterize the trees and cycles having this property Then we concentrate on double domination edge critical graphs having small double domination numbers. In particular, we characterize the ones with double domination number three and subfamilies of those with double domination number four.
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机译：在图形G =（V，E）中，如果V中的每个顶点至少被控制两次，则子集S C V为双控制集。 G的双控制集的最小基数是双控制数。如果对于任何边缘uv GE（G），G + uv的双支配数量小于G的双支配数量，则图G是双支配边缘临界。我们研究双“支配边缘临界图，并表征树和周期具有这个性质的我们将注意力集中在具有小的双支配数的双支配边临界图上，尤其是表征具有双支配数3的那些和具有双支配数4的子族。
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