Results 21 to 30 of about 1,439,443 (264)
Distinguishing numbers and distinguishing indices of oriented graphs
Discrete Applied Mathematics, 2020 A distinguishing r-vertex-labelling (resp. r-edge-labelling) of an undirected graph G is a mapping $ $ from the set of vertices (resp. the set of edges) of G to the set of labels {1,. .. , r} such that no non-trivial automorphism of G preserves all the vertex (resp. edge) labels.
Kahina Meslem, Éric Sopena
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On the Distinguishing Number of Functigraphs [PDF]
Symmetry, 2018 Let G 1 and G 2 be disjoint copies of a graph G and g : V ( G 1 ) → V ( G 2 ) be a function. A functigraph F G consists of the vertex set V ( G 1 ) ∪ V ( G 2 ) and the edge set E ( G 1 ) ∪ E ( G 2 ) ∪ { u v : g ( u ) = v } .
Muhammad Fazil +4 more
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Distinguishing homomorphisms of infinite graphs [PDF]
, 2012 We supply an upper bound on the distinguishing chromatic number of certain infinite graphs satisfying an adjacency property. Distinguishing proper $n$-colourings are generalized to the new notion of distinguishing homomorphisms. We prove that if a graph $
Bonato, Anthony, Delic, Dejan
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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 $G\not\cong K_{\Delta-1,\Delta}$, $K_{\Delta,\Delta}$.
Laflamme, C., Seyffarth, K.
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Adjacent vertex distinguishing acyclic edge coloring of the Cartesian product of graphs [PDF]
Transactions on Combinatorics, 2017 Let $G$ be a graph and $chi^{prime}_{aa}(G)$ denotes the minimum number of colors required for an acyclic edge coloring of $G$ in which no two adjacent vertices are incident to edges colored with the same set of colors. We prove a general bound for $
Fatemeh Sadat Mousavi, Massomeh Noori
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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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Impact of factor rotation on Q-methodology analysis
PLoS ONE, 2023 The Varimax and manual rotations are commonly used for factor rotation in Q-methodology; however, their effects on the results may not be well known.
Noori Akhtar-Danesh
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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
Cavers, Michael, Seyffarth, Karen
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Relations between the distinguishing number and some other graph parameters [PDF]
ریاضی و جامعهA distinguishing coloring of a simple graph $G$ is a vertex coloring of $G$ which is preserved only by the identity automorphism of $G$. In other words, this coloring ``breaks'' all symmetries of $G$.
Bahman Ahmadi +1 more
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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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