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Graphs and Combinatorics

, Volume 27, Issue 1, pp 129–141 | Cite as

The p-Bondage Number of Trees

  • You Lu
  • Jun-Ming XuEmail author
Original Paper

Abstract

Let p be a positive integer and G = (V, E) be a simple graph. A p-dominating set of G is a subset \({D\,{\subseteq}\, V}\) 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 \({B\subseteq E}\) for which γ p (GB) > 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.

Keywords

Domination Bondage number p-Domination p-Bondage number Trees 

Mathematics Subject Classification (2000)

05C69 

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Copyright information

© Springer 2010

Authors and Affiliations

  1. 1.Department of Applied MathematicsNorthwestern Polytechnical UniversityXi’anPeople’s Republic of China
  2. 2.Department of MathematicsUniversity of Science and Technology of ChinaHefeiPeople’s Republic of China

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