Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/13402
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dc.contributor.authorBatal, Ahmet-
dc.date.accessioned2023-04-19T12:39:46Z-
dc.date.available2023-04-19T12:39:46Z-
dc.date.issued2022-
dc.identifier.issn1303-5991-
dc.identifier.issn2618-6470-
dc.identifier.urihttps://doi.org/10.31801/cfsuasmas.1051208-
dc.identifier.urihttps://search.trdizin.gov.tr/yayin/detay/1146262-
dc.identifier.urihttps://hdl.handle.net/11147/13402-
dc.description.abstractFor a simple graph $G$ with vertex set $V(G)={v_1,...,v_n}$, we define the closed neighborhood set of a vertex $u$ as $N[u]={v in V(G) ; | ; v ; text{is adjacent to} ; u ; text{or} ; v=u }$ and the closed neighborhood matrix $N(G)$ as the matrix whose $i$th column is the characteristic vector of $N[v_i]$. We say a set $S$ is odd dominating if $N[u]cap S$ is odd for all $uin V(G)$. We prove that the parity of the cardinality of an odd dominating set of $G$ is equal to the parity of the rank of $G$, where rank of $G$ is defined as the dimension of the column space of $N(G)$. Using this result we prove several corollaries in one of which we obtain a general formula for the nullity of the join of graphs.en_US
dc.language.isoenen_US
dc.relation.ispartofCommunications Faculty of Sciences University of Ankara Series A1: Mathematics and Statisticsen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectLights outen_US
dc.subjectAll-ones problemen_US
dc.subjectOdd dominating seten_US
dc.subjectParity dominationen_US
dc.subjectDomination numberen_US
dc.titleParity of an odd dominating seten_US
dc.typeArticleen_US
dc.departmentİzmir Institute of Technology. Mathematicsen_US
dc.identifier.volume71en_US
dc.identifier.issue4en_US
dc.identifier.startpage1023en_US
dc.identifier.endpage1028en_US
dc.relation.publicationcategoryMakale - Ulusal Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.identifier.doi10.31801/cfsuasmas.1051208-
dc.identifier.trdizinid1146262en_US
item.openairetypeArticle-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.grantfulltextopen-
item.fulltextWith Fulltext-
item.languageiso639-1en-
item.cerifentitytypePublications-
crisitem.author.dept04.02. Department of Mathematics-
Appears in Collections:Mathematics / Matematik
TR Dizin İndeksli Yayınlar / TR Dizin Indexed Publications Collection
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