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On the rainbow vertex connection number of general unicyclic graphs
Journal of Discrete Mathematical Sciences & CryptographyIn a graph G, the distance between any two vertices is defined as the length of the shortest path connecting them. A path in G is termed rainbow vertex-connected if all internal vertices along the path have distinct colors. For every pair of vertices u and v in G, if there exists such a colored u-v path, the graph is considered rainbow vertex-connected.
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Rainbow Vertex Connection Numbers and Total Rainbow Connection Numbers of Middle and Total Graphs
Ars Combinatoria, 2023A vertex-colouring of a graph Γ is rainbow vertex connected if every pair of vertices ( u , v ) in Γ there is a u − v path whose internal vertices have different colours. The rainbow vertex connection number of a graph Γ , is the minimum number of colours needed to make Γ rainbow vertex connected, denoted by r v c ( Γ ) .
Yingbin Ma, Kairui Nie
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Rainbow vertex-connection and graph products
International Journal of Computer Mathematics, 2015A vertex-coloured graph G is said to be rainbow vertex-connected if every two vertices of G are connected by a path whose internal vertices have distinct colours, such a path is called a rainbow path. The rainbow vertex-connection number of a connected graph G, denoted by , is the smallest number of colours that are needed in order to make G rainbow
Yaping Mao +3 more
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Journal of Interconnection Networks, 2023
The proper rainbow vertex connection number of [Formula: see text], denoted by [Formula: see text], is the smallest number of colors needed to properly color the vertices of [Formula: see text] so that [Formula: see text] is rainbow vertex connected.
Yingbin Ma, Yanfeng Xue, Xiaoxue Zhang
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The proper rainbow vertex connection number of [Formula: see text], denoted by [Formula: see text], is the smallest number of colors needed to properly color the vertices of [Formula: see text] so that [Formula: see text] is rainbow vertex connected.
Yingbin Ma, Yanfeng Xue, Xiaoxue Zhang
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Rainbow vertex connection number of square, glue, middle and splitting graph of brush graph
AIP Conference Proceedings, 2020A vertex-colored graph G = (V(G), E(G)) is said a rainbow vertex-connected, if for every two vertices u and v in V(G), there exist a u−v path with all internal vertices have distinct colors. The rainbow vertex-connection number of G, denoted by rvc(G), is the smallest number of colors needed to make G rainbow vertex-connected.
Helmi Helmi +3 more
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Journal of Interconnection Networks
The proper rainbow vertex connection number of [Formula: see text], denoted by [Formula: see text], is the smallest number of colors needed to properly color the vertices of [Formula: see text] to make [Formula: see text] rainbow vertex connected. The proper strong rainbow vertex connection number of [Formula: see text], denoted by [Formula: see text],
Yingbin Ma, Yanfeng Xue, Xiaoxue Zhang
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The proper rainbow vertex connection number of [Formula: see text], denoted by [Formula: see text], is the smallest number of colors needed to properly color the vertices of [Formula: see text] to make [Formula: see text] rainbow vertex connected. The proper strong rainbow vertex connection number of [Formula: see text], denoted by [Formula: see text],
Yingbin Ma, Yanfeng Xue, Xiaoxue Zhang
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International Journal of Research and Innovation in Applied Science
The Rainbow Vertex Connection Number of a graph is the minimum number of colors required to make a graph rainbow vertex connected. A graph is said to be a rainbow vertex connected if there exists a rainbow vertex path between every pair of distinct vertices.
V. Jothika, P. Mythili
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The Rainbow Vertex Connection Number of a graph is the minimum number of colors required to make a graph rainbow vertex connected. A graph is said to be a rainbow vertex connected if there exists a rainbow vertex path between every pair of distinct vertices.
V. Jothika, P. Mythili
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Rainbow Vertex Connection Number of a Class of Triangular Snake Graph
2020Dharamvirsinh Parmar, Bharat Suthar
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Rainbow vertex-connection and graph products
International Journal of Computer Mathematics, 2016Yaping Mao, Chengfu Ye
exaly
Rainbow vertex -connection in graphs
Discrete Applied Mathematics, 2013Ângela Mestre, Teresa Sousa
exaly