Defensive k-alliances in graphs
| dc.creator | Rodriguez-Velazquez, J. A. | |
| dc.creator | Yero, I. G. | |
| dc.creator | Sigarreta, J. M. | |
| dc.date | 2006-11-07 | |
| dc.date | 2008-12-08 | |
| dc.date.accessioned | 2026-07-07T12:09:52Z | |
| dc.date.available | 2026-07-07T12:09:52Z | |
| dc.description | Let $Γ=(V,E)$ be a simple graph. For a nonempty set $X\subseteq V$, and a vertex $v\in V$, $δ_{X}(v)$ denotes the number of neighbors $v$ has in $X$. A nonempty set $S\subseteq V$ is a \emph{defensive $k$-alliance} in $Γ=(V,E)$ if $δ_S(v)\ge δ_{\bar{S}}(v)+k,$ $\forall v\in S.$ The defensive $k$-alliance number of $Γ$, denoted by $a_k(Γ)$, is defined as the minimum cardinality of a defensive $k$-alliance in $Γ$. We study the mathematical properties of $a_k(Γ)$. | |
| dc.identifier | https://arxiv.org/abs/math/0611180 | |
| dc.identifier | http://arxiv.org/abs/math/0611180 | |
| dc.identifier | Applied Mathematics Letters, 22 (2009) 96-100 | |
| dc.identifier | doi:10.1016/j.aml.2008.02.012 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/209778 | |
| dc.subject | Combinatorics | |
| dc.subject | 05C69; 05A20; 05C50 | |
| dc.title | Defensive k-alliances in graphs | |
| dc.type | text |