Results 11 to 20 of about 135,434 (260)
Graphs with Large Distinguishing Chromatic Number [PDF]
The Electronic Journal of Combinatorics, 2013 The distinguishing chromatic number $\chi_D(G)$ of a graph $G$ is the minimum number of colours required to properly colour the vertices of $G$ so that the only automorphism of $G$ that preserves colours is the identity. For a graph $G$ of order $n$, it is clear that $1\leq\chi_D(G)\leq n$, and it has been shown that $\chi_D(G)=n$ if and only if $G$ is
Cavers, Michael, Seyffarth, Karen
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Bounds on the Distinguishing Chromatic Number [PDF]
The Electronic Journal of Combinatorics, 2009 Collins and Trenk define the distinguishing chromatic number $\chi_D(G)$ of a graph $G$ to be the minimum number of colors needed to properly color the vertices of $G$ so that the only automorphism of $G$ that preserves colors is the identity. They prove results about $\chi_D(G)$ based on the underlying graph $G$.
Collins, Karen L. +2 more
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The Distinguishing Chromatic Number of Kneser Graphs [PDF]
The Electronic Journal of Combinatorics, 2013 A labeling $f: V(G) \rightarrow \{1, 2, \ldots, d\}$ of the vertex set of a graph $G$ is said to be proper $d$-distinguishing if it is a proper coloring of $G$ and any nontrivial automorphism of $G$ maps at least one vertex to a vertex with a different label.
Che, Zhongyuan, Collins, Karen L.
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Chromatic number is Ramsey distinguishing [PDF]
Journal of Graph Theory, 2021 AbstractA graph is Ramsey for a graph if every colouring of the edges of in two colours contains a monochromatic copy of . Two graphs and are Ramsey equivalent if any graph is Ramsey for if and only if it is Ramsey for . A graph parameter is Ramsey distinguishing if implies that and are not Ramsey equivalent.
M. Savery
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Nordhaus-Gaddum Theorem for the Distinguishing Chromatic Number [PDF]
The Electronic Journal of Combinatorics, 2013 Nordhaus and Gaddum proved, for any graph $G$, that $\chi(G) + \chi(\overline{G}) \leq n + 1$, where $\chi$ is the chromatic number and $n=|V(G)|$. Finck characterized the class of graphs, which we call NG-graphs, that satisfy equality in this bound. In this paper, we provide a new characterization of NG-graphs, based on vertex degrees, which yields a ...
Collins, Karen L., Trenk, Ann
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The edge-distinguishing chromatic number of petal graphs, chorded cycles, and spider graphs [PDF]
Electronic Journal of Graph Theory and Applications, 2022 23 pages, 1 ...
Grant Fickes, Wing Hong Tony Wong
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Neighbor Sum Distinguishing Total Chromatic Number of Graphs with Lower Average Degree
Journal of Mathematical Study, 2023 Summary: For a given simple graph \(G = (V(G),E(G)),\) a proper total-\(k\)-coloring \(c : V(G) \cup E(G) \rightarrow \{1,2,\dots,k\}\) is neighbor sum distinguishing if \(f(u) \neq f(v)\) for each edge \(uv \in E(G)\), where \(f(v) = \Sigma_{wv \in E(G)} c(wv)+c(v)\).
Huang, Danjun, Bao, Dan
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Upper Bounds for the List-Distinguishing Chromatic Number
Graphs and CombinatoricsAbstract In this paper, all results apply only to finite graphs. Let G be a simple connected finite graph with n vertices and maximum degree $$\Delta (G)$$ Δ ( G )
Amitayu Banerjee +2 more
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On Adjacent Vertex-distinguishing Total Chromatic Number of Generalized Mycielski Graphs
Taiwanese Journal of Mathematics, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhu, Enqiang, Liu, Chanjuan, Xu, Jin
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The distinguishing chromatic number of Cartesian products of two complete graphs
Discrete Mathematics, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jerebic, Janja, Klavžar, Sandi
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