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Distance-Local Rainbow Connection Number
Discussiones Mathematicae Graph Theory, 2022 Under an edge coloring (not necessarily proper), a rainbow path is a path whose edge colors are all distinct. The d-local rainbow connection number lrcd(G) (respectively, d-local strong rainbow connection number lsrcd(G)) is the smallest number of colors
Septyanto Fendy, Sugeng Kiki A.
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On Rainbow Antimagic Coloring of Joint Product of Graphs
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2023 Let be a connected graph with vertex set and edge set . A bijection from to the set is a labeling of graph . The bijection is called rainbow antimagic vertex labeling if for any two edge and in path , where and .
Brian Juned Septory +3 more
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Barekeng, 2023 Rainbow antimagic coloring is a combination of antimagic labeling and rainbow coloring. Antimagic labeling is labeling of each vertex of the graph with a different label, so that each the sum of the vertices in the graph has a different weight. Rainbow
R Adawiyah +4 more
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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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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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Jambura Journal of Mathematics, 2022 Rainbow vertex-connection number is the minimum k-coloring on the vertex graph G and is denoted by rvc(G). Besides, the rainbow-vertex connection number can be applied to some special graphs, such as prism graph and path graph.
Indrawati Lihawa +5 more
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Rainbow connection number of Cm o Pn and Cm o Cn
Indonesian Journal of Combinatorics, 2020 Let G = (V(G),E(G)) be a nontrivial connected graph. A rainbow path is a path which is each edge colored with different color. A rainbow coloring is a coloring which any two vertices should be joined by at least one rainbow path.
Alfi Maulani +3 more
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The rainbow 2-connectivity of Cartesian products of 2-connected graphs and paths
Electronic Journal of Graph Theory and Applications, 2020 An edge-colored graph G is rainbow k-connected, if there are k-internally disjoint rainbow paths connecting every pair of vertices of G. The rainbow k-connection number of G, denoted by rck(G), is the minimum number of colors needed for which there ...
Bety Hayat Susanti +2 more
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Proper Rainbow Connection Number of Graphs
Discussiones Mathematicae Graph Theory, 2021 A path in an edge-coloured graph is called a rainbow path if its edges receive pairwise distinct colours. An edge-coloured graph is said to be rainbow connected if any two distinct vertices of the graph are connected by a rainbow path.
Doan Trung Duy, Schiermeyer Ingo
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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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