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Discussiones Mathematicae Graph Theory 25(3) (2005) 391-406
DOI: https://doi.org/10.7151/dmgt.1291

AN UPPER BOUND OF THE BASIS NUMBER OF THE STRONG PRODUCT OF GRAPHS

Mohammed M.M. Jaradat

Department of Mathematics
Yarmouk University
Irbid-Jordan
e-mail: mmjst4@yu.edu.jo

Abstract

The basis number of a graph G is defined to be the least integer d such that there is a basis B of the cycle space of G such that each edge of G is contained in at most d members of B. In this paper we give an upper bound of the basis number of the strong product of a graph with a bipartite graph and we show that this upper bound is the best possible.

Keywords: basis number; cycle space; strong product.

2000 Mathematics Subject Classification: 05C38, 05C75.

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Received 29 June 2004
Revised 3 January 2005