On the automorphism groups of distance-regular graphs and rank-4\n primitive coherent configurations

2018/02/19 by Bohdan Kivva, Kivva, Bohdan
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1802.06959

openalex publication_date 2018/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The minimal degree of a permutation group G is the minimum number of points\nnot fixed by non-identity elements of G. Lower bounds on the minimal degree\nhave strong structural consequences on G. In 2014 Babai proved that the\nautomorphism group of a strongly regular graph with n vertices has minimal\ndegree \≥ c n, with known exceptions. Strongly regular graphs correspond to\nprimitive coherent configurations of rank 3. We extend Babai's result to\nprimitive coherent configurations of rank 4. We also show that the result\nextends to non-geometric distance-regular graphs of bounded diameter. The\nproofs combine structural and spectral methods.\n

Citations

• Graph Isomorphism in Quasipolynomial Time

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