Bell Numbers of Complete Multipartite Graphs
The {\it Stirling number} $S(G;k)$ is the number of partitions of the vertices of a graph $G$ into $k$ nonempty independent sets and the number of all partitions of $G$ is its {\it Bell number}, $B(G)$. We find $S(G;k)$ and $B(G)$ when $G$ is any complete multipartite graph, giving the upper bounds...
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| Format: | Article |
| Language: | English |
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Vladimir Andrunachievici Institute of Mathematics and Computer Science
2016-08-01
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| Series: | Computer Science Journal of Moldova |
| Subjects: | |
| Online Access: | http://www.math.md/files/csjm/v24-n2/v24-n2-(pp234-242).pdf |
| _version_ | 1828136358095355904 |
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| author | Julian Allagan Christopher Serkan |
| author_facet | Julian Allagan Christopher Serkan |
| author_sort | Julian Allagan |
| collection | DOAJ |
| description | The {\it Stirling number} $S(G;k)$ is the number of partitions of the vertices of a graph $G$ into $k$ nonempty independent sets and the number of all partitions of $G$ is its {\it Bell number}, $B(G)$. We find $S(G;k)$ and $B(G)$ when $G$ is any complete multipartite graph, giving the upper bounds of these parameters for any graph. |
| first_indexed | 2024-04-11T18:02:56Z |
| format | Article |
| id | doaj.art-47f3180f809e400ebf36d2a6f73cbeb6 |
| institution | Directory Open Access Journal |
| issn | 1561-4042 |
| language | English |
| last_indexed | 2024-04-11T18:02:56Z |
| publishDate | 2016-08-01 |
| publisher | Vladimir Andrunachievici Institute of Mathematics and Computer Science |
| record_format | Article |
| series | Computer Science Journal of Moldova |
| spelling | doaj.art-47f3180f809e400ebf36d2a6f73cbeb62022-12-22T04:10:25ZengVladimir Andrunachievici Institute of Mathematics and Computer ScienceComputer Science Journal of Moldova1561-40422016-08-01242(71)234242Bell Numbers of Complete Multipartite GraphsJulian Allagan0Christopher Serkan1University of North Georgia, Watkinsville, Georgia, U.S.AUniversity of North Georgia, Watkinsville, Georgia, U.S.AThe {\it Stirling number} $S(G;k)$ is the number of partitions of the vertices of a graph $G$ into $k$ nonempty independent sets and the number of all partitions of $G$ is its {\it Bell number}, $B(G)$. We find $S(G;k)$ and $B(G)$ when $G$ is any complete multipartite graph, giving the upper bounds of these parameters for any graph.http://www.math.md/files/csjm/v24-n2/v24-n2-(pp234-242).pdfBell numberBell polynomialPartitionStirling numbers |
| spellingShingle | Julian Allagan Christopher Serkan Bell Numbers of Complete Multipartite Graphs Computer Science Journal of Moldova Bell number Bell polynomial Partition Stirling numbers |
| title | Bell Numbers of Complete Multipartite Graphs |
| title_full | Bell Numbers of Complete Multipartite Graphs |
| title_fullStr | Bell Numbers of Complete Multipartite Graphs |
| title_full_unstemmed | Bell Numbers of Complete Multipartite Graphs |
| title_short | Bell Numbers of Complete Multipartite Graphs |
| title_sort | bell numbers of complete multipartite graphs |
| topic | Bell number Bell polynomial Partition Stirling numbers |
| url | http://www.math.md/files/csjm/v24-n2/v24-n2-(pp234-242).pdf |
| work_keys_str_mv | AT julianallagan bellnumbersofcompletemultipartitegraphs AT christopherserkan bellnumbersofcompletemultipartitegraphs |