Results 1 to 10 of about 4,256 (307)
Homogeneous colourings of graphs [PDF]
Mathematica Bohemica, 2023 A proper vertex $k$-colouring of a graph $G$ is called $l$-homogeneous if the number of colours in the neigbourhood of each vertex of $G$ equals $l$. We explore basic properties (the existence and the number of used colours) of homogeneous colourings of ...
Tomáš Madaras, Mária Šurimová
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A Greedy Technique Based Improved Approach to Solve Graph Colouring Problem [PDF]
EAI Endorsed Transactions on Scalable Information Systems, 2021 Graph colouring problem is a well-known NP-class optimization problem, studied due to a lot of applications in various real-world problems. Some of these applications are: register allocation, image processing and communication networks.
Ajay Shukla, Vishal Bharti, M. Garg
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Two-Step Colouring of Grid Graphs of Different Types
Моделирование и анализ информационных систем, 2022 In this article, we consider the NP-hard problem of the two-step colouring of a graph. It is required to colour the graph in a given number of colours in a way, when no pair of vertices has the same colour, if these vertices are at a distance of 1 or 2 ...
Alexander Valeryevich Smirnov
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Nonrepetitive Graph Colouring [PDF]
The Electronic Journal of Combinatorics, 2021 A vertex colouring of a graph $G$ is nonrepetitive if $G$ contains no path for which the first half of the path is assigned the same sequence of colours as the second half. Thue's famous theorem says that every path is nonrepetitively 3-colourable. This paper surveys results about nonrepetitive colourings of graphs.
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Edge Colouring of Neutrosophic Graphs and Its Application in Detection of Phishing Website
Discrete Dynamics in Nature and Society, 2022 Graph colouring enjoys many practical as well as theoretical uses. Graph colouring is still a very active subject of research. This article introduces a new concept of the chromatic number of the neutrosophic graph (NG).
Rupkumar Mahapatra +2 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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Colouring the Petals of a Graph [PDF]
The Electronic Journal of Combinatorics, 2003 A petal graph is a connected graph $G$ with maximum degree three, minimum degree two, and such that the set of vertices of degree three induces a $2$–regular graph and the set of vertices of degree two induces an empty graph. We prove here that, with the single exception of the graph obtained from the Petersen graph by deleting one vertex, all petal ...
Cariolaro, David, Cariolaro, Gianfranco
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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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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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