On the number of cut-vertices in a graph
A connected graph with n vertices contains no more than r2r-2(n-2) cutvertices of degree r. All graphs in which the bound is achieved are described. In addition, for graphs of maximum degree three and minimum δ, best possible bounds are obtained for δ=1, 2, 3.
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| Format: | Article |
| Language: | English |
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Hindawi Limited
1989-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171289000359 |
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Article |
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doaj-37073a56d72047ec87dd3110c662047c2020-11-25T00:59:43ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251989-01-0112230530810.1155/S0161171289000359On the number of cut-vertices in a graphGlenn Hopkins0William Staton1Department of Mathematics, University of Mississippi, University 38677, MS, USADepartment of Mathematics, University of Mississippi, University 38677, MS, USAA connected graph with n vertices contains no more than r2r-2(n-2) cutvertices of degree r. All graphs in which the bound is achieved are described. In addition, for graphs of maximum degree three and minimum δ, best possible bounds are obtained for δ=1, 2, 3.http://dx.doi.org/10.1155/S0161171289000359 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Glenn Hopkins William Staton |
| spellingShingle |
Glenn Hopkins William Staton On the number of cut-vertices in a graph International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Glenn Hopkins William Staton |
| author_sort |
Glenn Hopkins |
| title |
On the number of cut-vertices in a graph |
| title_short |
On the number of cut-vertices in a graph |
| title_full |
On the number of cut-vertices in a graph |
| title_fullStr |
On the number of cut-vertices in a graph |
| title_full_unstemmed |
On the number of cut-vertices in a graph |
| title_sort |
on the number of cut-vertices in a graph |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
1989-01-01 |
| description |
A connected graph with n vertices contains no more than r2r-2(n-2) cutvertices
of degree r. All graphs in which the bound is achieved are described. In
addition, for graphs of maximum degree three and minimum δ, best possible bounds are
obtained for δ=1, 2, 3. |
| url |
http://dx.doi.org/10.1155/S0161171289000359 |
| work_keys_str_mv |
AT glennhopkins onthenumberofcutverticesinagraph AT williamstaton onthenumberofcutverticesinagraph |
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1725216571658338304 |