Results 31 to 40 of about 82,445 (208)
On irreducible no-hole L(2, 1)-coloring of Cartesian product of trees with paths
AKCE International Journal of Graphs and Combinatorics, 2020 An L(2, 1)-coloring of a graph G is a mapping such that for all edges uv of G, and if u and v are at distance two in G. The span of an L(2, 1)-coloring f of G, denoted by span(f), is max The span of G, denoted by is the minimum span of all possible L(2 ...
Nibedita Mandal, Pratima Panigrahi
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Nonrepetitive colorings of graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 A vertex coloring of a graph $G$ is $k \textit{-nonrepetitive}$ if one cannot find a periodic sequence with $k$ blocks on any simple path of $G$. The minimum number of colors needed for such coloring is denoted by $\pi _k(G)$ . This idea combines graph colorings with Thue sequences introduced at the beginning of 20th century.
Noga Alon, Jarosław Grytczuk
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On the Total Set Chromatic Number of Graphs
Theory and Applications of Graphs, 2022 Given a vertex coloring c of a graph, the neighborhood color set of a vertex is defined to be the set of all of its neighbors’ colors. The coloring c is called a set coloring if any two adjacent vertices have different neighborhood color sets.
Mark Anthony C. Tolentino +2 more
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On Rainbow Antimagic Coloring of Joint Product of Graphs
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2023 Let be a connected graph with vertex set and edge set . A bijection from to the set is a labeling of graph . The bijection is called rainbow antimagic vertex labeling if for any two edge and in path , where and .
Brian Juned Septory +3 more
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Complexity of C_k-Coloring in Hereditary Classes of Graphs [PDF]
, 2019 For a graph F, a graph G is F-free if it does not contain an induced subgraph isomorphic to F. For two graphs G and H, an H-coloring of G is a mapping f:V(G) -> V(H) such that for every edge uv in E(G) it holds that f(u)f(v)in E(H).
Chudnovsky, Maria +4 more
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Solutions of Some L(2, 1)-Coloring Related Open Problems
Discussiones Mathematicae Graph Theory, 2016 An L(2, 1)-coloring (or labeling) of a graph G is a vertex coloring f : V (G) → Z+ ∪ {0} such that |f(u) − f(v)| ≥ 2 for all edges uv of G, and |f(u)−f(v)| ≥ 1 if d(u, v) = 2, where d(u, v) is the distance between vertices u and v in G.
Mandal Nibedita, Panigrahi Pratima
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Discrete Applied Mathematics, 1992 For directed graphs \(G=(V_ G,E_ G)\) and \(H=(V_ H,E_ H)\) an \(H\)- coloring of \(G\) is a mapping \(f:V_ G\to V_ H\) such that for all edges \((u,v)\in E_ G\) we have \((f(u),f(v))\in E_ H\). The authors introduce a new technique for proving that the \(H\)-coloring problem is polynomially solvable for some fixed digraphs \(H\).
Wolfgang Gutjahr +2 more
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On star and acyclic coloring of generalized lexicographic product of graphs
AIMS Mathematics, 2022 A $ star \; coloring $ of a graph $ G $ is a proper vertex coloring of $ G $ such that any path of length 3 in $ G $ is not bicolored. The $ star \; chromatic \; number $ $ \chi_s(G) $ of $ G $ is the smallest integer $ k $ for which $ G $ admits a star ...
Jin Cai, Shuangliang Tian, Lizhen Peng
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Topological and Graph-coloring Conditions on the Parameter-independent Stability of Second-order Networked Systems [PDF]
, 2017 In this paper, we study parameter-independent stability in qualitatively heterogeneous passive networked systems containing damped and undamped nodes.
Bürger, Mathias +3 more
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On facial unique-maximum (edge-)coloring [PDF]
, 2017 A facial unique-maximum coloring of a plane graph is a vertex coloring where on each face $\alpha$ the maximal color appears exactly once on the vertices of $\alpha$.
Andova, Vesna +4 more
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