On the basis of the direct product of paths and wheels
The basis number, b(G), of a graph G is defined to be the least integer k such that G has a k-fold basis for its cycle space. In this paper we determine the basis number of the direct product of paths and wheels. It is proved that P2∧Wn,is planar, and b(Pm∧Wn)=3, for all m≥3 and n≥4.
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| Format: | Article |
| Language: | English |
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Hindawi Limited
1996-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171296000580 |
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doaj-7c6d03c3e8aa46a8a0373f5951df3a502020-11-25T00:19:24ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251996-01-0119241141410.1155/S0161171296000580On the basis of the direct product of paths and wheelsA. A. Al-Rhayyel0Department of Mathematics, Yarmouk University, Irbid, JordanThe basis number, b(G), of a graph G is defined to be the least integer k such that G has a k-fold basis for its cycle space. In this paper we determine the basis number of the direct product of paths and wheels. It is proved that P2∧Wn,is planar, and b(Pm∧Wn)=3, for all m≥3 and n≥4.http://dx.doi.org/10.1155/S0161171296000580basis numbercycle spacepathsand wheels. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
A. A. Al-Rhayyel |
| spellingShingle |
A. A. Al-Rhayyel On the basis of the direct product of paths and wheels International Journal of Mathematics and Mathematical Sciences basis number cycle space paths and wheels. |
| author_facet |
A. A. Al-Rhayyel |
| author_sort |
A. A. Al-Rhayyel |
| title |
On the basis of the direct product of paths and wheels |
| title_short |
On the basis of the direct product of paths and wheels |
| title_full |
On the basis of the direct product of paths and wheels |
| title_fullStr |
On the basis of the direct product of paths and wheels |
| title_full_unstemmed |
On the basis of the direct product of paths and wheels |
| title_sort |
on the basis of the direct product of paths and wheels |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
1996-01-01 |
| description |
The basis number, b(G), of a graph G is defined to be the least integer k such that
G has a k-fold basis for its cycle space. In this paper we determine the basis number of the direct product
of paths and wheels. It is proved that P2∧Wn,is planar, and b(Pm∧Wn)=3, for all m≥3 and n≥4. |
| topic |
basis number cycle space paths and wheels. |
| url |
http://dx.doi.org/10.1155/S0161171296000580 |
| work_keys_str_mv |
AT aaalrhayyel onthebasisofthedirectproductofpathsandwheels |
| _version_ |
1725371606163783680 |