# Rainbow and strong rainbow connection number for some families of graphs

## DOI:

https://doi.org/10.22199/issn.0717-6279-2020-04-0046## Keywords:

Edge coloring, Rainbow coloring, Strong rainbow coloring## Abstract

Let G be a nontrivial connected graph. Then G is called a rainbow connected graph if there exists a coloring c : E(G) ? {1, 2, ..., k}, k ? N, of the edges of G, such that there is a u ? v rainbow path between every two vertices of G, where a path P in G is a rainbow path if no two edges of P are colored the same. The minimum k for which there exists such a k-edge coloring is the rainbow connection number rc(G) of G. If for every pair u, v of distinct vertices, G contains a rainbow u ? v geodesic, then G is called strong rainbow connected. The minimum k for which G is strong rainbow-connected is called the strong rainbow connection number src(G) of G. The exact rc and src of the rotationally symmetric graphs are determined.## References

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*Proyecciones (Antofagasta, On line)*, vol. 39, no. 4, pp. 737-747, Jul. 2020.

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Copyright (c) 2020 Yaqoub Ahmed Khan, Muhammad Naeem, Muhammad Kamran Siddiqui, Mohammad Reza Farahani

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