التفاصيل البيبلوغرافية
| العنوان: |
Partitioning a graph into defensive k-alliances |
| المؤلفون: |
Yero, Ismael G., Bermudo, Sergio, Rodriguez-Velazquez, Juan A., Sigarreta, Jose M. |
| سنة النشر: |
2009 |
| المجموعة: |
Mathematics |
| مصطلحات موضوعية: |
Mathematics - Combinatorics, 05C69 |
| الوصف: |
A defensive $k$-alliance in a graph is a set $S$ of vertices with the property that every vertex in $S$ has at least $k$ more neighbors in $S$ than it has outside of $S$. A defensive $k$-alliance $S$ is called global if it forms a dominating set. In this paper we study the problem of partitioning the vertex set of a graph into (global) defensive $k$-alliances. The (global) defensive $k$-alliance partition number of a graph $\Gamma=(V,E)$, ($\psi_{k}^{gd}(\Gamma)$) $\psi_k^{d}(\Gamma)$, is defined to be the maximum number of sets in a partition of $V$ such that each set is a (global) defensive $k$-alliance. We obtain tight bounds on $\psi_k^{d}(\Gamma)$ and $\psi_{k}^{gd}(\Gamma)$ in terms of several parameters of the graph including the order, size, maximum and minimum degree, the algebraic connectivity and the isoperimetric number. Moreover, we study the close relationships that exist among partitions of $\Gamma_1\times \Gamma_2$ into (global) defensive $(k_1+k_2)$-alliances and partitions of $\Gamma_i$ into (global) defensive $k_i$-alliances, $i\in \{1,2\}$. |
| نوع الوثيقة: |
Working Paper |
| DOI: |
10.1007/s10114-010-9075-6 |
| URL الوصول: |
http://arxiv.org/abs/0901.4923 |
| رقم الانضمام: |
edsarx.0901.4923 |
| قاعدة البيانات: |
arXiv |