Rainbow and strong rainbow connection number for some families of graphs
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...
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| Autores principales: | , , , |
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| Lenguaje: | English |
| Publicado: |
Universidad Católica del Norte, Departamento de Matemáticas
2020
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| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000400737 |
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| Sumario: | 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. |
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