Alliances and related parameters in graphs

Henning Fernau, Juan A. Rodriguez-Velazquez

Published 2013-11-19Version 1

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 propagation in 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 characterize various 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.