Emmanuel Breuillard, Ben J. Green, Robert Guralnick, Terence Tao (2015)
Journal of the European Mathematical Society
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We show that random Cayley graphs of finite simple (or semisimple) groups of Lie type of fixed rank are expanders. The proofs are based on the Bourgain-Gamburd method and on the main result of our companion paper [BGGT].
Droms, Carl, Servatius, Brigitte, Servatius, Herman (1998)
Beiträge zur Algebra und Geometrie
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S. Shalchi, A. Erfanian, M. Farrokhi DG (2017)
Open Mathematics
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The θ-commutators of elements of a group with respect to an automorphism are introduced and their properties are investigated. Also, corresponding to θ-commutators, we define the θ-non-commuting graphs of groups and study their correlations with other notions. Furthermore, we study independent sets in θ-non-commuting graphs, which enable us to evaluate the chromatic number of such graphs.
Ustimenko, V.A. (2005)
Zapiski Nauchnykh Seminarov POMI
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W. Wessel (1987)
Applicationes Mathematicae
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L.M. Lopez (1994)
Discrete & computational geometry
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Bretto, A. (1999)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Zdzisław Skupień (2007)
Discussiones Mathematicae Graph Theory
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Šiagiová, J., Simanjuntak, R. (2004)
Acta Mathematica Universitatis Comenianae. New Series
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Risto Šokarovski (1977)
Publications de l'Institut Mathématique
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Mieczysław Borowiecki, Peter Mihók, Zsolt Tuza, M. Voigt (1999)
Discussiones Mathematicae Graph Theory
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We consider the problem of the existence of uniquely partitionable planar graphs. We survey some recent results and we prove the nonexistence of uniquely (𝓓₁,𝓓₁)-partitionable planar graphs with respect to the property 𝓓₁ "to be a forest".
Alain Bretto, Alain Faisant (2005)
Mathematica Slovaca
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Xuanlong Ma, Kaishun Wang (2016)
Discussiones Mathematicae Graph Theory
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For any positive integer k, let Ak denote the set of finite abelian groups G such that for any subgroup H of G all Cayley sum graphs CayS(H, S) are integral if |S| = k. A finite abelian group G is called Cayley sum integral if for any subgroup H of G all Cayley sum graphs on H are integral. In this paper, the classes A2 and A3 are classified. As an application, we determine all finite Cayley sum integral groups.
Igor' E. Zverovich, Olga I. Zverovich (2004)
Discussiones Mathematicae Graph Theory
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We introduce a new hereditary class of graphs, the dominant-matching graphs, and we characterize it in terms of forbidden induced subgraphs.