Rainbow and strong rainbow connection number for some families of graphs

Authors

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.

Author Biographies

Yaqoub Ahmed Khan, Government College University.

Dept. of Mathematics.

Muhammad Naeem, Institute of Southern Punjab.

Dept. of Mathematics and Statistics.

Muhammad Kamran Siddiqui, Comsats University Islamabad.

Dept. of Mathematics.

Mohammad Reza Farahani, Iran University of Science and Technology.

Dept. of Applied Mathematics.

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Published

2020-07-28

How to Cite

[1]
Y. A. Khan, M. Naeem, M. K. Siddiqui, and M. R. Farahani, “Rainbow and strong rainbow connection number for some families of graphs”, Proyecciones (Antofagasta, On line), vol. 39, no. 4, pp. 737-747, Jul. 2020.