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An updated survey on rainbow connections of graphs - a dynamic survey
Theory and Applications of Graphs, 2017 The concept of rainbow connection was introduced by Chartrand, Johns, McKeon and Zhang in 2008. Nowadays it has become a new and active subject in graph theory. There is a book on this topic by Li and Sun in 2012, and a survey paper by Li, Shi and Sun in
Xueliang Li, Yuefang Sun
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Rainbow vertex-connection number of 2-connected graphs [PDF]
, 2011 The {\em rainbow vertex-connection number}, $rvc(G)$, of a connected graph $G$ is the minimum number of colors needed to color its vertices such that every pair of vertices is connected by at least one path whose internal vertices have distinct colors ...
Zhiping Wang, Yi-Xiao Liu, Xiao-Jing Xu
semanticscholar +1 more source
Developing A Secure Cryptosystem with Rainbow Vertex Antimagic Coloring of Cycle Graph [PDF]
, 2022 An edge labeling of graph G is a function g from the edge set of graph G to the first natural numbers up to the number of the edge set. Graph G admits a rainbow vertex antimagic coloring if, for any two vertices, there is a path with different colors of ...
Marsidi, Marsidi
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The rainbow vertex connection number of edge corona product graphs
IOP Conference Series: Earth and Environment, 2019 Let G1, G2 be a special graphs with vertices of G1 1,2,…, n and edges of G1 1,2,… m. The generalized edge corona product of graphs G1 and G2, denoted by G1 ⋄ G1 is obtained by taking one copy of graph G1 and m copy of G2, thus for each edge ek = ij of G,
D. A. Fauziah +3 more
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Total Rainbow Connection Number Of Shackle Product Of Antiprism Graph (〖AP〗_3)
Jurnal Matematika Statistika dan Komputasi, 2023 Function if is said to be k total rainbows in , for each pair of vertex there is a path called with each edge and each vertex on the path will have a different color.
Melisa Huntala +2 more
semanticscholar +1 more source
Vertex rainbow colorings of graphs [PDF]
, 2012 In a properly vertex-colored graph G, a path P is a rainbow path if no two vertices of P have the same color, except possibly the two end-vertices of P. If every two vertices of G are connected by a rainbow path, then G is vertex rainbow-connected.
Fujie-Okamoto, Futaba +3 more
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Generalized Rainbow Connection of Graphs and their Complements
Discussiones Mathematicae Graph Theory, 2018 Let G be an edge-colored connected graph. A path P in G is called ℓ-rainbow if each subpath of length at most ℓ + 1 is rainbow. The graph G is called (k, ℓ)-rainbow connected if there is an edge-coloring such that every pair of distinct vertices of G is ...
Li Xueliang +3 more
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Rainbow connection number of generalized composition
AKCE International Journal of Graphs and Combinatorics, 2020 Let be a connected graph with . The rainbow connection number is the smallest for which there is a map such that any two vertices can be connected by a path whose edge colors are all distinct.
Fendy Septyanto, Kiki Ariyanti Sugeng
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A Note on Extendable Sets of Colorings and Rooted Minors
Journal of Graph Theory, EarlyView.ABSTRACT DeVos and Seymour proved that for every set C $C$ of 3‐colorings of a set X $X$ of vertices, there exists a plane graph G $G$ with vertices of X $X$ incident with the outer face such that a 3‐coloring of X $X$ extends to a 3‐coloring of G $G$ if and only if it belongs to C $C$.
Zdeněk Dvořák, Jan M. Swart
wiley +1 more source
Simultaneous Network Design With Restricted Link Usage
Networks, EarlyView.ABSTRACT Given a digraph with two terminal vertices s$$ s $$ and t$$ t $$ as well as a conservative cost function and several not necessarily disjoint color classes on its arc set, our goal is to find a minimum‐cost subset of the arcs such that its intersection with each color class contains an s$$ s $$‐t$$ t $$ dipath.
Naonori Kakimura +3 more
wiley +1 more source