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Zbl 0673.05050
Ali, Ali A.
The basis numbers of the direct products of paths and cycles. (English)
[J] Ars Comb. 27, 155-164 (1989). ISSN 0381-7032

The basis number, b(G), of a graph G is defined to be the least integer h such that G has an h-fold basis for its cycle space. In this paper we determine the basis number of the direct products of paths and cycles. It is proved that $b(C\sb m\cdot P\sb n)\le 2$ and $b(C\sb m\cdot C\sb n)=3$.
[A.A.Ali]

MSC 2000:: *05C35 Extremal problems (graph theory)
05C38 Paths and cycles

Keywords: basis number; cycle space; direct products of paths and cycles

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Zentralblatt MATH Berlin [Germany]