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A function f:V->{-1,1} defined on the vertices of a graph G=(V,E) is a signed 2-independence function if the sum of its function values over any closed neighbourhood is at most one. That is, for every v V, f(N[v])=<1, where N[v] consists of v and every vertex adjacent to v. The weight of a signed 2-independence function is f(V)= f(v), over all vertices v V. The signed 2-independence number...
The k-restricted domination number of a graph G is the smallest integer d k such that given any subset U of k vertices of G, there exists a dominating set of G of cardinality at most d k containing U. Hence, the k-restricted domination number of a graph G measures how many vertices are necessary to dominate a graph if an arbitrary set of k vertices must be included in the dominating...
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