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Desimal, 2021 A graph is said rainbow connected if no path has more than one vertices of the same color inside. The minimum number of colors required to make a graph to be rainbow vertex-connected is called rainbow vertex connection-number and denoted by rvc(G ...
Afifah Farhanah Akadji +3 more
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Barekeng, 2023 Rainbow vertex-connection number is the minimum colors assignment to the vertices of the graph, such that each vertex is connected by a path whose edges have distinct colors and is denoted by .
Nisky Imansyah Yahya +3 more
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The Rainbow (Vertex) Connection Number of Pencil Graphs
Procedia Computer Science, 2015 AbstractAn edge colored graph G = (V(G), E(G)) is said rainbow connected, if any two vertices are connnected by a path whose edges have distinct colors. The rainbow connection number of G, denoted by rc(G), is the smallest positive integer of colors needed in order to make G rainbow connected. The vertex-colored graph G is said rainbow vertex-connected,
A N M Salman
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THE RAINBOW VERTEX-CONNECTION NUMBERS OF WHEEL-SHIELD GRAPHS
BarekengLet be a nontrivial simple connected graph, be an edge of and be an integer greater than or equal to . A path of order , denoted by , is a graph whose vertices can be labelled such that .
Ratnaning Palupi, A. N. M. Salman
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BarekengThe rainbow connection was first introduced by Chartrand in 2006 and then in 2009 Krivelevich and Yuster first time introduced the rainbow vertex connection. Let graph be a connected graph.
Muhammad Ilham Nurfaizi Annadhifi +3 more
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The Vertex-Rainbow Connection Number of Some Graph Operations
Discussiones Mathematicae Graph Theory, 2021 A path in an edge-colored (respectively vertex-colored) graph G is rainbow (respectively vertex-rainbow) if no two edges (respectively internal vertices) of the path are colored the same.
Li Hengzhe, Ma Yingbin, Li Xueliang
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The Rainbow Vertex-Connection Number of Star Fan Graphs [PDF]
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2018 A vertex-colored graph is said to be rainbow vertex-connected, if for every two vertices and in , there exists a path with all internal vertices have distinct colors.
Ariestha Widyastuty Bustan +1 more
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Rainbow connections of bioriented graphs [PDF]
HeliyonFor a directed graph D, it's deemed rainbow connected if each arc is assigned a different color, so that all paths from the vertex u to the vertex v are rainbow connected.
Linlin Wang, Sujuan Liu, Han Jiang
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Rainbow Vertex-Connection and Forbidden Subgraphs
Discussiones Mathematicae Graph Theory, 2018 A path in a vertex-colored graph is called vertex-rainbow if its internal vertices have pairwise distinct colors. A vertex-colored graph G is rainbow vertex-connected if for any two distinct vertices of G, there is a vertex-rainbow path connecting them ...
Li Wenjing, Li Xueliang, Zhang Jingshu
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Further hardness results on the rainbow vertex-connection number of graphs
Theoretical Computer Science, 2013 A vertex-colored graph $G$ is {\it rainbow vertex-connected} if any pair of vertices in $G$ are connected by a path whose internal vertices have distinct colors, which was introduced by Krivelevich and Yuster. The {\it rainbow vertex-connection number} of a connected graph $G$, denoted by $rvc(G)$, is the smallest number of colors that are needed in ...
Lily Chen, Xueliang Li
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