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Rainbow Connection Number of Graphs with Diameter 3
Discussiones Mathematicae Graph Theory, 2017 A path in an edge-colored graph G is rainbow if no two edges of the path are colored the same. The rainbow connection number rc(G) of G is the smallest integer k for which there exists a k-edge-coloring of G such that every pair of distinct vertices of G
Li Hengzhe, Li Xueliang, Sun Yuefang
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Oriented diameter and rainbow connection number of a graph [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 Graph ...
Xiaolong Huang +3 more
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Rainbow connection number of amalgamation of some graphs
AKCE International Journal of Graphs and Combinatorics, 2016 Let G be a nontrivial connected graph. For k∈N, we define a coloring c:E(G)→{1,2,…,k} of the edges of G such that adjacent edges can be colored the same. A path P in G is a rainbow path if no two edges of P are colored the same. A rainbow path connecting
D. Fitriani, A.N.M. Salman
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Rainbow connection number of corona product of graphs
Electronic Journal of Graph Theory and ApplicationsIn an edge-colored graph (where adjacent edges may have the same color), a rainbow path is a path whose edge colors are all distinct. The coloring is called a rainbow coloring if any two vertices can be connected by a rainbow path. The rainbow connection
Fendy Septyanto
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Rainbow Connection Numbers of WK-Recursive Networks and WK-Recursive Pyramids
MathematicsAn edge coloring of a graph G results in G being rainbow connected when every pair of vertices is linked by a rainbow path. Such a path is defined as one where each edge possesses a distinct color.
Fu-Hsing Wang, Cheng-Ju Hsu
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Rainbow Connection Number and Connectivity [PDF]
The Electronic Journal of Combinatorics, 2012 The rainbow connection number, $rc(G)$, of a connected graph $G$ is the minimum number of colors needed to color its edges, so that every pair of vertices is connected by at least one path in which no two edges are colored the same. Our main result is that $rc(G)\leq \lceil\frac{n}{2}\rceil$ for any 2-connected graph with at least three vertices.
Xueliang Li 0001 +4 more
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Rainbow Connection Number and Radius [PDF]
Graphs and Combinatorics, 2012 The rainbow connection number, rc(G), of a connected graph G is the minimum number of colours needed to colour its edges, so that every pair of its vertices is connected by at least one path in which no two edges are coloured the same. In this note we show that for every bridgeless graph G with radius r, rc(G) <= r(r + 2).
Manu Basavaraju +3 more
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Rainbow Connection Number and the Number of Blocks [PDF]
Graphs and Combinatorics, 2013 7 ...
Xueliang Li 0001, Sujuan Liu
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Rainbow Connection Number and Connected Dominating Sets [PDF]
Electronic Notes in Discrete Mathematics, 2011 AbstractThe rainbow connection number of a connected graph is the minimum number of colors needed to color its edges, so that every pair of its vertices is connected by at least one path in which no two edges are colored the same. In this article we show that for every connected graph on n vertices with minimum degree δ, the rainbow connection number ...
L. Sunil Chandran +3 more
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Upper bounding rainbow connection number by forest number [PDF]
Discrete Mathematics, 2022 A path in an edge-colored graph is rainbow if no two edges of it are colored the same, and the graph is rainbow-connected if there is a rainbow path between each pair of its vertices. The minimum number of colors needed to rainbow-connect a graph $G$ is the rainbow connection number of $G$, denoted by $\text{rc}(G)$.
L. Sunil Chandran +3 more
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