Results 31 to 40 of about 1,439,443 (264)
Local Finiteness, Distinguishing Numbers, and Tucker's Conjecture [PDF]
The Electronic Journal of Combinatorics, 2015 A distinguishing colouring of a graph is a colouring of the vertex set such that no non-trivial automorphism preserves the colouring. Tucker conjectured that if every non-trivial automorphism of a locally finite graph moves infinitely many vertices, then there is a distinguishing 2-colouring.
Lehner, Florian, Möller, Rögnvaldur G.
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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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On multiset colorings of generalized corona graphs [PDF]
Mathematica Bohemica, 2016 A vertex $k$-coloring of a graph $G$ is a \emph{multiset $k$-coloring} if $M(u)\neq M(v)$ for every edge $uv\in E(G)$, where $M(u)$ and $M(v)$ denote the multisets of colors of the neighbors of $u$ and $v$, respectively. The minimum $k$ for which $G$ has
Yun Feng, Wensong Lin
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Neighbor Distinguishing Colorings of Graphs with the Restriction for Maximum Average Degree
Axioms, 2023 Neighbor distinguishing colorings of graphs represent powerful tools for solving the channel assignment problem in wireless communication networks. They consist of two forms of coloring: neighbor distinguishing edge coloring, and neighbor distinguishing ...
Jingjing Huo +3 more
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Focused verbal inflections in Spanish
Isogloss, 2021 Spanish allows to focus the Number and Person features of the verbal inflection to produce an interpretation similar to that of a contrastively focused pronoun. This squib discusses two properties distinguishing both phenomena.
Carlos Muñoz Pérez, Matías Verdecchia
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Adjacent Vertex Distinguishing Coloring of Fuzzy Graphs
Mathematics, 2023 In this paper, we consider the adjacent vertex distinguishing proper edge coloring (for short, AVDPEC) and the adjacent vertex distinguishing total coloring (for short, AVDTC) of a fuzzy graph.
Zengtai Gong, Chen Zhang
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The distinguishing number and the distinguishing index of co-normal product of two graphs
Ratio Mathematica, 2019 The distinguishing number (index) $D(G)$ ($D'(G)$) of a graph $G$ is the least integer $d$ such that $G$ has an vertex labeling (edge labeling) with $d$ labels that is preserved only by a trivial automorphism.
Saeid Alikhani, Samaneh Soltani
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Characterization of graphs with distinguishing number equal list distinguishing number
, 2017 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 a trivial automorphism. A list assignment to $G$ is an assignment $L = \{L(v)\}_{v\in V (G)}$ of lists of labels to the vertices of $G$. A distinguishing $L$-labeling of $G$ is a distinguishing labeling
Alikhani, Saeid, Soltani, Samaneh
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Distinguishing Numbers for Graphs and Groups [PDF]
The Electronic Journal of Combinatorics, 2004 A graph $G$ is distinguished if its vertices are labelled by a map $\phi: V(G) \longrightarrow \{1,2,\ldots, k\}$ so that no non-trivial graph automorphism preserves $\phi$. The distinguishing number of $G$ is the minimum number $k$ necessary for $\phi$ to distinguish the graph. It measures the symmetry of the graph.
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Distinguishing number and adjacency properties [PDF]
Journal of Combinatorics, 2010 One of the most widely studied infinite graphs is the Rado or infinite random graph, written R. A graph satisfies the existentially closed or e.c. adjacency property if for all finite disjoint sets of vertices A and B (one of which may be empty), there is a vertex z / ∈ A ∪ B joined to all of A and to no vertex of B.
Anthony Bonato, Dejan Delic
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