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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| Published in: | Electronic journal of graph theory and applications Vol. 2; no. 1; pp. 70 - 86 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia
01.01.2014
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| Subjects: | |
| ISSN: | 2338-2287, 2338-2287 |
| Online Access: | Get full text |
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| Summary: | 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. |
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| ISSN: | 2338-2287 2338-2287 |
| DOI: | 10.5614/ejgta.2014.2.1.7 |