id: 05999818
dt: j
an: 05999818
au: Lu, You; Xu, Jun-Ming
ti: The $p$-bondage number of trees.
so: Graphs Comb. 27, No. 1, 129-141 (2011).
py: 2011
pu: Springer-Verlag, Tokyo
la: EN
cc: 
ut: Domination; Bondage number; $p$-Domination; $p$-Bondage number; Trees
ci: 
li: doi:10.1007/s00373-010-0956-3
ab: Summary: 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 $Δ(G) \geq p$ is the
    minimum cardinality among all sets of edges $B \subseteq E$ for which
    $γ_{p}(G-B) > γ_{p}(G)$. For any integer $p \geq 2$ and tree $T$ with
    $Δ(T) \geq p$, this paper shows that $1 \leq b _{p}(T) \leq
    Δ(T)-p+1$, and characterizes all trees achieving the equalities.
rv: