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Full-Text Articles in Physical Sciences and Mathematics
On A Vizing-Type Integer Domination Conjecture, Elliot Krop, Randy R. Davila
On A Vizing-Type Integer Domination Conjecture, Elliot Krop, Randy R. Davila
Theory and Applications of Graphs
Given a simple graph G, a dominating set in G is a set of vertices S such that every vertex not in S has a neighbor in S. Denote the domination number, which is the size of any minimum dominating set of G, by γ(G). For any integer k ≥ 1, a function f : V (G) → {0, 1, . . ., k} is called a {k}-dominating function if the sum of its function values over any closed neighborhood is at least k. The weight of a {k}-dominating function is the sum of its values over all …