Total Rainbow Connection Number of Some Graph Operations
Axioms, 2022 In a graph H with a total coloring, a path Q is a total rainbow if all elements in V(Q)∪E(Q), except for its end vertices, are assigned different colors. The total coloring of a graph H is a total rainbow connected coloring if, for any x,y∈V(H), there is
Hengzhe Li, Yingbin Ma, Yan Zhao
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RAINBOW CONNECTION NUMBER AND TOTAL RAINBOW CONNECTION NUMBER OF AMALGAMATION RESULTS DIAMOND GRAPH(〖Br〗_4) AND FAN GRAPH(F_3) [PDF]
Barekeng, 2022 If be a graph and edge coloring of G is a function , rainbow connection number is the minimum-k coloration of the rainbow on the edge of graph G and denoted by rc(G). Rainbow connection numbers can be applied to the result of operations on some special
Sumarno Ismail +3 more
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Rainbow Total-Coloring of Complementary Graphs and Erdős-Gallai Type Problem For The Rainbow Total-Connection Number [PDF]
Discussiones Mathematicae Graph Theory, 2018 A total-colored graph G is rainbow total-connected if any two vertices of G are connected by a path whose edges and internal vertices have distinct colors.
Sun Yuefang, Jin Zemin, Tu Jianhua
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Total Rainbow Connection Number Of Shackle Product Of Antiprism Graph (〖AP〗_3) [PDF]
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. The total connection number is denoted by trc defined as the minimum number of colors needed to make graph to be total rainbow connected. Total rainbow connection numbers can also be
Melisa Huntala +2 more
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Hardness Results for Total Rainbow Connection of Graphs [PDF]
Discussiones Mathematicae Graph Theory, 2016 A total-colored path is total rainbow if both its edges and internal vertices have distinct colors. The total rainbow connection number of a connected graph G, denoted by trc(G), is the smallest number of colors that are needed in a total-coloring of G ...
Chen Lily, Huo Bofeng, Ma Yingbin
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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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On the rainbow connection numbers of line, middle, and total graphs of wheels
Electronic Journal of Graph Theory and ApplicationsAn edge-colored graph G is called rainbow connected if any two vertices in G are connected by a path whose no two edges are colored the same. The rainbow connection of G, denoted by rc(G), is the smallest number of colors needed such that G be a rainbow ...
Lyra Yulianti +2 more
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Tight Nordhaus–Gaddum-Type Upper Bound for Total-Rainbow Connection Number of Graphs [PDF]
Results in Mathematics, 2017 20 ...
Li, Wenjing +3 more
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Total Rainbow Connection Number of Corona Product of Book Graph(Bn) and Pencil Graf(Pcm)
Sainsmat : Jurnal Ilmiah Ilmu Pengetahuan Alam, 2023 Let G be a simple and finite graph. Rainbow connection and total rainbow connection c are set c : G → {1,2,. . . , k} where k is the minimal color on graph G. A rainbow connection number(rc) is a pattern by giving different colors to the connection edges (E(G)) so that a rainbow path is formed.
Randi Mooduto +2 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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