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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Universidad Católica del Norte, Departamento de Matemáticas
2020
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oai:scielo:S0716-091720200004007372020-08-13Rainbow and strong rainbow connection number for some families of graphsKhan,Yaqoub AhmedNaeem,MuhammadSiddiqui,Muhammad KamranFarahani,Mohammad Reza 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.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.39 n.4 20202020-08-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000400737en10.22199/issn.0717-6279-2020-04-0046 |
| institution |
Scielo Chile |
| collection |
Scielo Chile |
| language |
English |
| topic |
Edge coloring Rainbow coloring Strong rainbow coloring |
| spellingShingle |
Edge coloring Rainbow coloring Strong rainbow coloring Khan,Yaqoub Ahmed Naeem,Muhammad Siddiqui,Muhammad Kamran Farahani,Mohammad Reza Rainbow and strong rainbow connection number for some families of graphs |
| description |
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 |
Khan,Yaqoub Ahmed Naeem,Muhammad Siddiqui,Muhammad Kamran Farahani,Mohammad Reza |
| author_facet |
Khan,Yaqoub Ahmed Naeem,Muhammad Siddiqui,Muhammad Kamran Farahani,Mohammad Reza |
| author_sort |
Khan,Yaqoub Ahmed |
| title |
Rainbow and strong rainbow connection number for some families of graphs |
| title_short |
Rainbow and strong rainbow connection number for some families of graphs |
| title_full |
Rainbow and strong rainbow connection number for some families of graphs |
| title_fullStr |
Rainbow and strong rainbow connection number for some families of graphs |
| title_full_unstemmed |
Rainbow and strong rainbow connection number for some families of graphs |
| title_sort |
rainbow and strong rainbow connection number for some families of graphs |
| publisher |
Universidad Católica del Norte, Departamento de Matemáticas |
| publishDate |
2020 |
| url |
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000400737 |
| work_keys_str_mv |
AT khanyaqoubahmed rainbowandstrongrainbowconnectionnumberforsomefamiliesofgraphs AT naeemmuhammad rainbowandstrongrainbowconnectionnumberforsomefamiliesofgraphs AT siddiquimuhammadkamran rainbowandstrongrainbowconnectionnumberforsomefamiliesofgraphs AT farahanimohammadreza rainbowandstrongrainbowconnectionnumberforsomefamiliesofgraphs |
| _version_ |
1718439875464658944 |