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VGU RESEARCH REPOSITORY


Please use this identifier to cite or link to this item: https://epub.vgu.edu.vn/handle/dlibvgu/49
DC FieldValueLanguage
dc.contributor.authorHoang Thach Nguyenen_US
dc.contributor.authorTran Thi Thu Huongen_US
dc.date.accessioned2020-03-12T16:53:52Z-
dc.date.available2020-03-12T16:53:52Z-
dc.date.issued2018-
dc.identifier.urihttp://epub.vgu.edu.vn/handle/dlibvgu/49-
dc.description.abstractAval et al. proved in Aval et al. (2016) that starting from a critical configuration of a chip-firing game on an undirected graph, one can never achieve a stable configuration by reverse firing any non-empty subsets of its vertices. In this paper, we generalize the result to digraphs with a global sink where reverse firing subsets of vertices is replaced with reverse firing multi-subsets of vertices. Consequently, a combinatorial proof for the duality between critical configurations and superstable configurations on digraphs is given. Finally, by introducing the concept of energy vector assigned to each configuration, we show that critical and superstable configurations are the unique ones with the greatest and smallest (w.r.t. the containment order), respectively, energy vectors in each of their equivalence classes.en_US
dc.language.isoenen_US
dc.publisherElsevier, Science Directen_US
dc.relation.ispartofseriesDiscrete Applied Mathematics;Vol.250105-
dc.subjectCritical configurationsen_US
dc.subjectSuperstable configurationsen_US
dc.subjectDualityChip-firing gamesen_US
dc.subjectEnergy vector optimizeren_US
dc.titleA maximizing characteristic for critical configurations of chip-firing games on digraphsen_US
dc.typeArticleen_US
dc.identifier.doi10.1016/j.dam.2018.05.005-
dc.relation.journaltypeISI (SCI) Q2en_US
item.fulltextNo Fulltext-
item.languageiso639-1other-
item.grantfulltextnone-
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