A survey on alliances and related parameters in graphs
FB 4-Abteilung Informatikwissenschaften, Universit ̈ at Trier, 54286 Trier, Germany, Henning Fernau, Juan Alberto Rodriguez-Velazquez, Departament d Enginyeria Informatica i Matematiques, Universitat Rovira i Virgili, Av. Paısos Catalans 26, 43007 Tarragona, Spain · Electronic Journal of Graph Theory and Applications · 2014
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.