Results 31 to 40 of about 650 (167)
On the inverse graph of a finite group and its rainbow connection number
Electronic Journal of Graph Theory and Applications, 2023 A rainbow path in an edge-colored graph G is a path that every two edges have different colors. The minimum number of colors needed to color the edges of G such that every two distinct vertices are connected by a rainbow path is called the rainbow ...
Rian Febrian Umbara +2 more
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The rainbow connection number of the enhanced power graph of a finite group
Electronic Journal of Graph Theory and Applications, 2023 Let G be a finite group. The enhanced power graph ΓGe of G is the graph with vertex set G and two distinct vertices are adjacent if they generate a cyclic subgroup of G. In this article, we calculate the rainbow connection number of ΓGe.
Luis A. Dupont +2 more
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(1, 2)-rainbow connection number at most 3 in connected dense graphs
Electronic Journal of Graph Theory and Applications, 2023 Let G be an edge-coloured connected graph G. A path P in the graph G is called l-rainbow path if each subpath of length at most l + 1 is rainbow. The graph G is called (k, l)-rainbow connected if any two vertices in G are connected by at least k pairwise
Trung Duy Doan, Le Thi Duyen
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On the Locating Rainbow Connection Number of Trees and Regular Bipartite Graphs [PDF]
, 2023 Locating the rainbow connection number of graphs is a new mathematical concept that combines the concepts of the rainbow vertex coloring and the partition dimension.
Putri, Pritta E. +7 more
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Upper bounding rainbow connection number by forest number [PDF]
, 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.
Lauri, Juho +3 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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Distance-Local Rainbow Connection Number
, 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
Sugeng, Kiki A., Septyanto, Fendy
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The rainbow connection problem: Mathematical formulations
, 2016 The concept of rainbow connection was introduced by Chartrand et al. in 2008. The rainbow connection number, rc(G), of a connected graph G = (V, E) is the minimum number of colors needed to color the edges of E, so that each pair of the vertices in V is ...
Kutucu H., Nuriyeva F., Ugurlu O.
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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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