Rainbow and strong rainbow connection number for some families of graphs

Khan, Yaqoub Ahmed ; Naeem, Muhammad ^[3] ; Siddiqui, Muhammad Kamran ^[1] ; Farahani, Mohammad Reza ^[2]
1. [1] COMSATS Institute of Information Technology
  
  COMSATS Institute of Information Technology
  
  Pakistán
2. [2] Iran University of Science and Technology
  
  Iran University of Science and Technology
  
  Irán
3. [3] Institute of Southern Punjab.
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Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 39, Nº. Extra 4, 2020 (Ejemplar dedicado a: Special Issue: Mathematical Computation in Combinatorics and Graph Theory; i), págs. 737-747
Idioma: inglés
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Resumen
- 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.