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On Adjacent Vertex-distinguishing Total Chromatic Number of Generalized Mycielski Graphs [PDF]
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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A note on the adjacent vertex distinguishing total chromatic number of graphs [PDF]
Discrete Mathematics, 2012 Adjacent vertex distinguishing total coloring of given graph \(G\) is a coloring \(\phi :V(G) \cup E(G) \rightarrow \{1,2,\dots,k\}\) such that \(\phi(x) \neq \phi(y)\) for any adjacent or incident elements \(x,y \in V(G) \cup E(G)\) and moreover \(C_\phi(x) \neq C_\phi(y)\) for any adjacent vertices \(x\) and \(y\), where \(C_\phi(x) = \{\phi(xy) \mid
Danjun Huang +2 more
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On the graphs with distinguishing number equal list distinguishing number [PDF]
Journal of Mahani Mathematical Research, 2023 The distinguishing number $D(G)$ of a graph $G$ is the least integer $d$ such that $G$ has an vertex labeling with $d$ labels that is preserved only by the trivial automorphism.
Saeid Alikhani, Samaneh Soltani
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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.
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The Distinguishing Chromatic Number [PDF]
The Electronic Journal of Combinatorics, 2006 In this paper we define and study the distinguishing chromatic number, $\chi_D(G)$, of a graph $G$, building on the work of Albertson and Collins who studied the distinguishing number. We find $\chi_D(G)$ for various families of graphs and characterize those graphs with $\chi_D(G)$ $ = |V(G)|$, and those trees with the maximum chromatic distingushing ...
Karen L. Collins, Ann N. Trenk
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AVD proper edge-coloring of some families of graphs
International Journal of Mathematics for Industry, 2021 Adjacent vertex-distinguishing proper edge-coloring is the minimum number of colors required for the proper edge-coloring of [Formula: see text] in which no two adjacent vertices are incident to edges colored with the same set of colors.
J. Naveen
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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 $G$.
Karen L. Collins +2 more
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Distinguishing Chromatic Numbers of Bipartite Graphs [PDF]
The Electronic Journal of Combinatorics, 2009 Extending the work of K.L. Collins and A.N. Trenk, we characterize connected bipartite graphs with large distinguishing chromatic number. In particular, if $G$ is a connected bipartite graph with maximum degree $\Delta \geq 3$, then $\chi_D(G)\leq 2\Delta -2$ whenever $G\not\cong K_{\Delta-1,\Delta}$, $K_{\Delta,\Delta}$.
Claude Laflamme, Karen Seyffarth
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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
Michael S. Cavers, Karen Seyffarth
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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.
Zhongyuan Che, Karen L. Collins
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