A survey on alliances and related parameters in graphs

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...

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Veröffentlicht in:	Electronic journal of graph theory and applications Jg. 2; H. 1; S. 70 - 86
Hauptverfasser:	Fernau, Henning, Rodrıguez-Velazquez, Juan A.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia 01.01.2014
Schlagworte:	alliances in graphs computational complexity of graph problems domination in graphs graph parameters
ISSN:	2338-2287, 2338-2287
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	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.
ISSN:	2338-2287 2338-2287
DOI:	10.5614/ejgta.2014.2.1.7