Signed k-independence in graphs
Lutz Volkmann (2014)
Open Mathematics
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Let k ≥ 2 be an integer. A function f: V(G) → −1, 1 defined on the vertex set V(G) of a graph G is a signed k-independence function if the sum of its function values over any closed neighborhood is at most k − 1. That is, Σx∈N[v] f(x) ≤ k − 1 for every v ∈ V(G), where N[v] consists of v and every vertex adjacent to v. The weight of a signed k-independence function f is w(f) = Σv∈V(G) f(v). The maximum weight w(f), taken over all signed k-independence functions f on G, is the signed k-independence...