The p-Bondage Number of Trees |
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Authors: | You Lu Jun-Ming Xu |
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Institution: | (1) Universit? Pierre et Marie Curie, E. Combinatoire, Case 189, 4 Place Jussieu, 75005 Paris, France;(2) CELC/Universidade de Lisboa, Faculdade de Ci?ncias, Campo Grande, edif?cio C6 - Piso 2, 1749-016 Lisboa, Portugal |
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Abstract: | Let p be a positive integer and G = (V, E) be a simple graph. A p-dominating set of G is a subset D í V{D\,{\subseteq}\, V} such that every vertex not in D has at least p neighbors in D. The p-domination number of G is the minimum cardinality of a p-dominating set of G. The p-bondage number of a graph G with (ΔG) ≥ p is the minimum cardinality among all sets of edges B í E{B\subseteq E} for which γ
p
(G − B) > γ
p
(G). For any integer p ≥ 2 and tree T with (ΔT) ≥ p, this paper shows that 1 ≤ b
p
(T) ≤ (ΔT) − p + 1, and characterizes all trees achieving the equalities. |
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Keywords: | |
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