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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1291,
author = {Mohammed M.M. Jaradat},
title = {An upper bound of the basis number of the strong product of graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {25},
year = {2005},
pages = {391-406},
zbl = {1107.05049},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1291}
}
Mohammed M.M. Jaradat. An upper bound of the basis number of the strong product of graphs. Discussiones Mathematicae Graph Theory, Tome 25 (2005) pp. 391-406. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1291/
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