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The authors are partially supported by the Program for the Promotion of International Research by Ritsumeikan University and grants FEDER/Ministerio de Ciencia, Innovacion y Universidades/AEI/MTM2017-89686-P; and Xunta de Galicia/ED431C 2019/10. We would also like to thank the anonymous referee for a careful reading of the paper.

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Lijo, Ramon BarralCorresponding Author

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June 22, 2024
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Coarse distinguishability of graphs with symmetric growth

Publicated to:Ars Mathematica Contemporanea. 21 (1): P1.06- - 2021-01-01 21(1), DOI: 10.26493/1855-3974.2354.616

Authors: Alvarez Lopez, Jesus Antonio; Lijo, Ramon Barral; Nozawa, Hiraku

Affiliations

Ritsumeikan Univ, Dept Math Sci, Coll Engn, Nojihigashi 1-1-1, Kusatsu, Shiga 5258577, Japan - Author
Ritsumeikan Univ, Dept Math Sci, Coll Sci, Nojihigashi 1-1-1, Kusatsu, Shiga 5258577, Japan - Author
Ritsumeikan Univ, Res Org Sci & Technol, Nojihigashi 1-1-1, Kusatsu, Shiga 5258577, Japan - Author
Univ Santiago de Compostela, Fac Matemat, Dept & Inst Matemat, Santiago De Compostela 15782, Spain - Author

Abstract

Let X be a connected, locally finite graph with symmetric growth. We prove that there is a vertex coloring phi: X -> {0, 1} and some R is an element of N such that every automorphism f preserving phi is R-close to the identity map; this can be seen as a coarse geometric version of symmetry breaking. We also prove that the infinite motion conjecture is true for graphs where at least one vertex stabilizer S-x satisfies the following condition: for every nonidentity automorphism f is an element of S-x, there is a sequence x(n) such that lim d(x(n), f(x(n))) = infinity.

Keywords

CoarseColoringDifferentiationDistinguishingGraphGrowthProductRandom-walksSymmetr

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Ars Mathematica Contemporanea due to its progression and the good impact it has achieved in recent years, according to the agency Scopus (SJR), it has become a reference in its field. In the year of publication of the work, 2021, it was in position , thus managing to position itself as a Q2 (Segundo Cuartil), in the category Algebra and Number Theory. Notably, the journal is positioned en el Cuartil Q3 for the agency WoS (JCR) in the category Mathematics.

Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-07-27:

  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 1 (PlumX).

Leadership analysis of institutional authors

This work has been carried out with international collaboration, specifically with researchers from: Japan.

the author responsible for correspondence tasks has been BARRAL LIJO, RAMON.