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A study of applications of graph colouring in various fields
International Journal of Statistics and Applied Mathematics, 2022 Graph theory is an important branch of applied mathematics with a lot of applications in many fields. Graph theory has a broad scale of applications in many practical situations.
Anjali Gangrade +3 more
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Fuzzy dominator coloring on fuzzy soft graphs
Ratio Mathematica, 2023 A fuzzy soft dominator colouring of a fuzzy soft graph $G^S$(T,V) is an appropriate fuzzy soft colouring such that every single vertex of $G^S$(T,V) dominate entire vertex of a colour group.
Jahir Hussain Rasheed, Afya Farhana
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The Metric Chromatic Number of Zero Divisor Graph of a Ring Zn
International Journal of Mathematics and Mathematical Sciences, 2022 Let Γ be a nontrivial connected graph, c:VΓ⟶ℕ be a vertex colouring of Γ, and Li be the colouring classes that resulted, where i=1,2,…,k. A metric colour code for a vertex a of a graph Γ is ca=da,L1,da,L2,…,da,Ln, where da,Li is the minimum distance ...
Husam Qasem Mohammad +2 more
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Acyclic, Star and Oriented Colourings of Graph Subdivisions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 Let G be a graph with chromatic number χ (G). A vertex colouring of G is \emphacyclic if each bichromatic subgraph is a forest. A \emphstar colouring of G is an acyclic colouring in which each bichromatic subgraph is a star forest. Let χ _a(G) and χ _s(G)
David R. Wood
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Graph Colouring Meets Deep Learning: Effective Graph Neural Network Models for Combinatorial Problems [PDF]
IEEE International Conference on Tools with Artificial Intelligence, 2019 Deep learning has consistently defied state-of-the-art techniques in many fields over the last decade. However, we are just beginning to understand the capabilities of neural learning in symbolic domains. Deep learning architectures that employ parameter
Henrique Lemos +3 more
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Colouring diamond-free graphs [PDF]
Journal of Computer and System Sciences, 2017 The Colouring problem is that of deciding, given a graph $G$ and an integer $k$, whether $G$ admits a (proper) $k$-colouring. For all graphs $H$ up to five vertices, we classify the computational complexity of Colouring for $(\mbox{diamond},H)$-free graphs.
Konrad K. Dabrowski +2 more
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On \delta^(k)-colouring of Powers of Paths and Cycles
Theory and Applications of Graphs, 2021 In a proper vertex colouring of a graph, the vertices are coloured in such a way that no two adjacent vertices receive the same colour, whereas in an improper vertex colouring, adjacent vertices are permitted to receive same colours subjected to some ...
Merlin Ellumkalayil, Sudev Naduvath
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Problems and results on graph and hypergraph colouring
Le Matematiche, 1990 See directly the article.
Szolt Tuza
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Defective and Clustered Graph Colouring [PDF]
, 2018 Consider the following two ways to colour the vertices of a graph where the requirement that adjacent vertices get distinct colours is relaxed. A colouring has "defect" $d$ if each monochromatic component has maximum degree at most $d$.
D. Wood
semanticscholar +1 more source
Universal H-Colourable Graphs [PDF]
Graphs and Combinatorics, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Broere, Izak, Heidema, Johannes
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