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Efficient Domination In Knights Graphs, Anne Sinko, Peter J. Slater

Mathematics Faculty Publications

The influence of a vertex set S ⊆V(G) is I(S) = Σ_v∈S(1 + deg(v)) = Σ_v∈S |N[v]|, which is the total amount of domination done by the vertices in S. The efficient domination number F(G) of a graph G is equal to the maximum influence of a packing, that is, F(G) is the maximum number of vertices one can dominate under the restriction that no vertex gets dominated more than once.

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