The rainbow 2-connectivity of Cartesian products of 2-connected graphs and paths

Bety Hayat Susanti, A.N.M. Salman, Rinovia Simanjuntak


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 rck(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.


Cartesian product, 2-connected graph, rainbow $2$-connectivity, rainbow path

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