# A Survey on Alliances and Related Parameters in Graphs

Henning Fernau • Juan A. Rodriguez-Velazquez

## Abstrak

In this paper, we show that several graph parameters are known in different areas under completely different names.More specifically, our observations connect signed domination, monopolies, $\alpha$-domination, $\alpha$-independence,positive influence domination,and a parameter associated to fast information propagationin networks to parameters related to various notions of global $r$-alliances in graphs.We also propose a new framework, called (global) $(D,O)$-alliances, not only in order to characterizevarious known variants of alliance and domination parameters, but also to suggest a unifying framework for the study of alliances and domination.Finally, we also give a survey on the mentioned graph parameters, indicating how results transfer due to our observations.

### Metrics

• 124 kali dilihat
• 59 kali diunduh

### Jurnal

Electronic Journal of Graph Theory and Applications

The Electronic Journal of Graph Theory and Applications (EJGTA) is a refereed journal devoted to ... tampilkan semua