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Relevant bibliographies by topics / Graph edge-coloring

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Journal articles

Academic literature on the topic 'Graph edge-coloring'

Author: Grafiati

Published: 4 June 2021

Last updated: 6 September 2023

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Journal articles on the topic "Graph edge-coloring"

1

Zhong, Chuang, and Shuangliang Tian. "Neighbor Sum Distinguishing Edge (Total) Coloring of Generalized Corona Product." Journal of Physics: Conference Series 2381, no. 1 (2022): 012031. http://dx.doi.org/10.1088/1742-6596/2381/1/012031.

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Abstract The coloring theory of graphs is an important part of graph theory research. The key problem of the coloring theory of graphs is to determine the coloring number of each kind of coloring. Traditional coloring concepts mainly include proper vertex coloring, proper edge coloring, proper total coloring, and so on. In recent years, scholars at home and abroad have put forward some new coloring concepts, such as neighbor vertex distinguishing edge (total) coloring, and neighbor sum distinguishing edge (total) coloring, based on traditional coloring concepts and by adding other constraints.

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2

Bagheri Gh., Behrooz, and Behnaz Omoomi. "On the simultaneous edge coloring of graphs." Discrete Mathematics, Algorithms and Applications 06, no. 04 (2014): 1450049. http://dx.doi.org/10.1142/s1793830914500499.

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A μ-simultaneous edge coloring of graph G is a set of μ proper edge colorings of G with a same color set such that for each vertex, the sets of colors appearing on the edges incident to that vertex are the same in each coloring and no edge receives the same color in any two colorings. The μ-simultaneous edge coloring of bipartite graphs has a close relation with μ-way Latin trades. Mahdian et al. (2000) conjectured that every bridgeless bipartite graph is 2-simultaneous edge colorable. Luo et al. (2004) showed that every bipartite graphic sequence S with all its elements greater than one, has

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3

Sedlar, Jelena, and Riste Škrekovski. "Remarks on the Local Irregularity Conjecture." Mathematics 9, no. 24 (2021): 3209. http://dx.doi.org/10.3390/math9243209.

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A locally irregular graph is a graph in which the end vertices of every edge have distinct degrees. A locally irregular edge coloring of a graph G is any edge coloring of G such that each of the colors induces a locally irregular subgraph of G. A graph G is colorable if it allows a locally irregular edge coloring. The locally irregular chromatic index of a colorable graph G, denoted by χirr′(G), is the smallest number of colors used by a locally irregular edge coloring of G. The local irregularity conjecture claims that all graphs, except odd-length paths, odd-length cycles and a certain class

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4

Piri, Mohammad R., and Saeid Alikhani. "Introduction to dominated edge chromatic number of a graph." Opuscula Mathematica 41, no. 2 (2021): 245–57. http://dx.doi.org/10.7494/opmath.2021.41.2.245.

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We introduce and study the dominated edge coloring of a graph. A dominated edge coloring of a graph \(G\), is a proper edge coloring of \(G\) such that each color class is dominated by at least one edge of \(G\). The minimum number of colors among all dominated edge coloring is called the dominated edge chromatic number, denoted by \(\chi_{dom}^{\prime}(G)\). We obtain some properties of \(\chi_{dom}^{\prime}(G)\) and compute it for specific graphs. Also examine the effects on \(\chi_{dom}^{\prime}(G)\), when \(G\) is modified by operations on vertex and edge of \(G\). Finally, we consider the

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5

K.S, Kanzul Fathima, and Jahir Hussain R. "An Introduction to Fuzzy Edge Coloring." JOURNAL OF ADVANCES IN MATHEMATICS 11, no. 10 (2016): 5742–48. http://dx.doi.org/10.24297/jam.v11i10.801.

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In this paper, a new concept of fuzzy edge coloring is introduced. The fuzzy edge coloring is an assignment of colors to edges of a fuzzy graph G. It is proper if no two strong adjacent edges of G will receive the same color. Fuzzy edge chromatic number of G is least positive integer for which G has a proper fuzzy edge coloring. In this paper, the fuzzy edge chromatic number of different classes of fuzzy graphs and the fuzzy edge chromatic number of fuzzy line graphs are found. Isochromatic fuzzy graph is also defined.

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6

Erzurumluoğlu, Aras, and C. A. Rodger. "On Evenly-Equitable, Balanced Edge-Colorings and Related Notions." International Journal of Combinatorics 2015 (March 4, 2015): 1–7. http://dx.doi.org/10.1155/2015/201427.

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A graph G is said to be even if all vertices of G have even degree. Given a k-edge-coloring of a graph G, for each color i∈Zk={0,1,…,k-1} let G(i) denote the spanning subgraph of G in which the edge-set contains precisely the edges colored i. A k-edge-coloring of G is said to be an even k-edge-coloring if for each color i∈Zk, G(i) is an even graph. A k-edge-coloring of G is said to be evenly-equitable if for each color i∈Zk, G(i) is an even graph, and for each vertex v∈V(G) and for any pair of colors i,j∈Zk, |degG(i)(v)-degG(j)(v)|∈{0,2}. For any pair of vertices {v,w} let mG({v,w}) be the num

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7

Furmańczyk, Hanna, Adrian Kosowski, Bernard Ries, and Paweł Żyliński. "Mixed graph edge coloring." Discrete Mathematics 309, no. 12 (2009): 4027–36. http://dx.doi.org/10.1016/j.disc.2008.11.033.

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8

Adawiyah, Robiatul, Indi Izzah Makhfudloh, and Rafiantika Megahnia Prihandini. "Local edge (a, d) –antimagic coloring on sunflower, umbrella graph and its application." Alifmatika: Jurnal Pendidikan dan Pembelajaran Matematika 5, no. 1 (2023): 70–81. http://dx.doi.org/10.35316/alifmatika.2023.v5i1.70-81.

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Suppose a graph G = (V, E) is a simple, connected and finite graph with vertex set V(G) and an edge set E(G). The local edge antimagic coloring is a combination of local antimagic labelling and edge coloring. A mapping f∶ V (G)→ {1, 2, ..., |V (G)|} is called local edge antimagic coloring if every two incident edges e_1and e_2, then the edge weights of e_1and e_2 maynot be the same, w(e_1) ≠ w(e_2), with e = uv ∈ G, w(e) = f(u)+ f(v) with the rule that the edges e are colored according to their weights, w_e. Local edge antimagic coloring has developed into local (a,d)-antimagic coloring. Local

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9

HUC, FLORIAN. "WEIGHTED-EDGE-COLORING OF k-DEGENERATE GRAPHS AND BIN-PACKING." Journal of Interconnection Networks 12, no. 01n02 (2011): 109–24. http://dx.doi.org/10.1142/s0219265911002861.

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The weighted-edge-coloring problem of an edge-weighted graph whose weights are between 0 and 1, consists in finding a coloring using as few colors as possible and satisfying the following constraints: the sum of weights of edges with the same color and incident to the same vertex must be at most 1. In 1991, Chung and Ross conjectured that if G is bipartite, then [Formula: see text] colors are always sufficient to weighted-edge-color (G,w), where [Formula: see text] is the maximum of the sums of the weights of the edges incident to a vertex. We prove this is true for edge-weighted graphs with m

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10

Li, Minhui, Shumin Zhang, Caiyun Wang, and Chengfu Ye. "The Dominator Edge Coloring of Graphs." Mathematical Problems in Engineering 2021 (October 7, 2021): 1–7. http://dx.doi.org/10.1155/2021/8178992.

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Let G be a simple graph. A dominator edge coloring (DE-coloring) of G is a proper edge coloring in which each edge of G is adjacent to every edge of some color class (possibly its own class). The dominator edge chromatic number (DEC-number) of G is the minimum number of color classes among all dominator edge colorings of G , denoted by χ d ′ G . In this paper, we establish the bounds of the DEC-number of a graph, present the DEC-number of special graphs, and study the relationship of the DEC-number between G and the operations of G .

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