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Strong edge colorings of graphs
Discrete Mathematics, 1996 The strong coloring number of a graph \(G\), \(\chi_s'(G)\), is the minimum number of colors for which there is a proper edge-coloring of \(G\) so that no two vertices are incident to edges having the same set of colors. (It is assumed that \(G\) has no isolated edges and at most one isolated vertex.) {Burris} and Schelp [J.
Odile Favaron +2 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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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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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.
Saeed Akbari, Hoda Bidkhori, N. Nosrati
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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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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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Between proper and strong edge‐colorings of subcubic graphs [PDF]
Journal of Graph Theory, 2020 AbstractIn a proper edge‐coloring the edges of every color form a matching. A matching is induced if the end‐vertices of its edges induce a matching. A strong edge‐coloring is an edge‐coloring in which the edges of every color form an induced matching.
Hervé Hocquard +2 more
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Strong edge colorings of graphs and the covers of Kneser graphs [PDF]
Journal of Graph Theory, 2022 AbstractA proper edge coloring of a graph is strong if it creates no bichromatic path of length three. It is well known that for a strong edge coloring of a ‐regular graph at least colors are needed. We show that a ‐regular graph admits a strong edge coloring with colors if and only if it covers the Kneser graph .
Borut Luzar +3 more
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Characterizations of Graphs Having Large Proper Connection Numbers
Discussiones Mathematicae Graph Theory, 2016 Let G be an edge-colored connected graph. A path P is a proper path in G if no two adjacent edges of P are colored the same. If P is a proper u − v path of length d(u, v), then P is a proper u − v geodesic. An edge coloring c is a proper-path coloring of
Lumduanhom Chira +2 more
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