Rainbow and strong rainbow connection number for some families of graphs
Author
Khan, Yaqoub Ahmed
Naeem, Muhammad
Siddiqui, Muhammad Kamran
Farahani, Mohammad Reza
Full text
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/424910.22199/issn.0717-6279-2020-04-0046
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.