Abstract
An edge-colored graph G is rainbow k-connected , if there are k -internally disjoint rainbow paths connecting every pair of vertices of G . The rainbow k -connection number of G , denoted by rc k (G) , is the minimum number of colors needed for which there exists a rainbow k -connected coloring for G . In this paper, we are able to find sharp lower and upper bounds for the rainbow 2-connection number of Cartesian products of arbitrary 2-connected graphs and paths. We also determine the rainbow 2-connection number of the Cartesian products of some graphs, i.e. complete graphs, fans, wheels, and cycles, with paths.
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