Parity of an odd dominating set
| dc.contributor.author | Batal, Mehmet | |
| dc.contributor.department | Other | tr_TR |
| dc.contributor.faculty | Other | tr_TR |
| dc.date.accessioned | 2022-12-29T10:48:29Z | |
| dc.date.available | 2022-12-29T10:48:29Z | |
| dc.date.issued | 2022 | |
| dc.description.abstract | For 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 ∈ V ( G ) | v is adjacent to u 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 ] ∩ S is odd for all u ∈ 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. | tr_TR |
| dc.description.index | Trdizin | tr_TR |
| dc.identifier.endpage | 1028 | tr_TR |
| dc.identifier.issn/e-issn | 1303-5991 | |
| dc.identifier.issue | 4 | tr_TR |
| dc.identifier.startpage | 1023 | tr_TR |
| dc.identifier.uri | https://doi.org/10.31801/cfsuasmas.1051208 | tr_TR |
| dc.identifier.uri | http://hdl.handle.net/20.500.12575/86611 | |
| dc.identifier.volume | 71 | tr_TR |
| dc.language.iso | en | tr_TR |
| dc.publisher | Ankara Üniversitesi | tr_TR |
| dc.relation.isversionof | 10.31801/cfsuasmas.1051208 | tr_TR |
| dc.relation.journal | Communications, Series A1:Mathematics and Statistics | tr_TR |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Başka Kurum Yazarı | tr_TR |
| dc.subject | Lights out, all-ones problem, odd dominating set, parity domination, domination number | tr_TR |
| dc.title | Parity of an odd dominating set | tr_TR |
| dc.type | Article | tr_TR |
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