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2002•Random Structures and AlgorithmsRequires access

On the asymmetry of random regular graphs and random graphs

Jeong Han Kim, Benny Sudakov, Van H. Vu

Open publisher page 80 citations

Abstract

Abstract This paper studies the symmetry of random regular graphs and random graphs. Our main result shows that for all 3 ≤ d ≤ n − 4 the random d‐regular graph on n vertices almost surely has no nontrivial automorphisms. This answers an open question of N. Wormald [13]. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 21: 216–224, 2002

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What this paper is about

Abstract This paper studies the symmetry of random regular graphs and random graphs. Our main result shows that for all 3 ≤ d ≤ n − 4 the random d‐regular graph on n vertices almost surely has no nontrivial automorphisms. This answers an open question of N. Wormald [13]. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 21: 216–224, 2002

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OpenAlex reports 80 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Abstract This paper studies the symmetry of random regular graphs and random graphs. Our main result shows that for all 3 ≤ d ≤ n − 4 the random d‐regular graph on n vertices almost surely has no nontrivial automorphisms. This answers an open question of N. Wormald [13]. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 21: 216–224, 2002

Key concepts: Random regular graph, Random graph, struct, Mathematics, Combinatorics, Automorphism, Discrete mathematics, Indifference graph

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