Results 11 to 20 of about 4,925 (221)
Exact square coloring of graphs resulting from some graph operations and products
AKCE International Journal of Graphs and Combinatorics, 2022 A vertex coloring of a graph [Formula: see text] is called an exact square coloring of G if any pair of vertices at distance 2 receive distinct colors.
Priyamvada, B. S. Panda
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The strong 3-rainbow index of edge-comb product of a path and a connected graph
Electronic Journal of Graph Theory and Applications, 2022 Let G be a connected and edge-colored graph of order n, where adjacent edges may be colored the same. A tree in G is a rainbow tree if all of its edges have distinct colors. Let k be an integer with 2 ≤ k ≤ n.
Zata Yumni Awanis +2 more
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Graphs with Strong Proper Connection Numbers and Large Cliques
Axioms, 2023 In this paper, we mainly investigate graphs with a small (strong) proper connection number and a large clique number. First, we discuss the (strong) proper connection number of a graph G of order n and ω(G)=n−i for 1⩽i⩽3. Next, we investigate the rainbow
Yingbin Ma, Xiaoxue Zhang, Yanfeng Xue
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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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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 Strong 3-Rainbow Index of Graphs Containing Three Cycles
InPrime, 2023 The concept of a strong k-rainbow index is a generalization of a strong rainbow connection number, which has an interesting application in security systems in a communication network.
Zata Yumni Awanis
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r-Strong edge colorings of graphs
Discrete Mathematics, 2006 If \(G\) is a graph and \(n\) a natural number, \(\chi(G,n)\) denotes the minimum number of colours required for a proper edge colouring of \(G\) in which no two vertices with distance at most \(n\) are incident to edges coloured with the same set of colours.
Akbari, S., Bidkhori, H., Nosrati, N.
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Strong edge-coloring of planar graphs
Discrete Mathematics, 2014 A strong edge coloring of a graph is a proper edge coloring where the edges at distance at most two receive distinct colors. It is known that every planar graph with maximum degree D has a strong edge coloring with at most 4D + 4 colors. We show that 3D + 6 colors suffice if the graph has girth 6, and 3D colors suffice if the girth is at least 7 ...
Hudák, Dávid +3 more
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Strong edge-coloring of 2-degenerate graphs
Discrete Applied Mathematics, 2023 A strong edge-coloring of a graph $G$ is an edge-coloring in which every color class is an induced matching, and the strong chromatic index $χ_s'(G)$ is the minimum number of colors needed in strong edge-colorings of $G$. A graph is $2$-degenerate if every subgraph has minimum degree at most $2$. Choi, Kim, Kostochka, and Raspaud (2016) showed $χ_s'(G)
Gexin Yu, Rachel Yu
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On the Adjacent Strong Equitable Edge Coloring of Pn ∨ Pn, Pn ∨ Cn and Cn ∨ Cn
MATEC Web of Conferences, 2016 A proper edge coloring of graph G is called equitable adjacent strong edge coloring if colored sets from every two adjacent vertices incident edge are different,and the number of edges in any two color classes differ by at most one,which the required ...
Liu Jun +4 more
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