Geodesic
Minimal cycle bases of the lexicographic product of graphs
Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 2, pp. 229-247

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A construction of minimum cycle bases of the lexicographic product of graphs is presented. Moreover, the length of a longest cycle of a minimal cycle basis is determined.
Keywords: cycle space, lexicographic product, cycle basis 
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     author = {Jaradat, M.},
     title = {Minimal cycle bases of the lexicographic product of graphs},
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Jaradat, M. Minimal cycle bases of the lexicographic product of graphs. Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 2, pp. 229-247. http://geodesic.mathdoc.fr/item/DMGT_2008_28_2_a2/