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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Wiley
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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| _version_ | 1832562677212250112 |
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| author | A. A. Al-Rhayyel |
| author_facet | A. A. Al-Rhayyel |
| author_sort | A. A. Al-Rhayyel |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-7c6d03c3e8aa46a8a0373f5951df3a50 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1996-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-7c6d03c3e8aa46a8a0373f5951df3a502025-02-03T01:22:08ZengWileyInternational 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. |
| 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. |
| title | 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_short | On the basis of the direct product of paths and wheels |
| title_sort | on the basis of the direct product of paths and wheels |
| topic | basis number cycle space paths and wheels. |
| url | http://dx.doi.org/10.1155/S0161171296000580 |
| work_keys_str_mv | AT aaalrhayyel onthebasisofthedirectproductofpathsandwheels |