Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the spectral gap and the automorphism group of distance-regular
  graphs   We prove that a distance-regular graph with a dominant distance is a spectral
expander. The key ingredient of the proof is a new inequality on the
intersection numbers. We use the spectral gap bound to study the structure of
the automorphism group.
  The minimal degree of a permutation group $G$ is the minimum number of points
not fixed by non-identity elements of $G$. Lower bounds on the minimal degree
have strong structural consequences on $G$. In 2014 Babai proved that the
automorphism group of a strongly regular graph with $n$ vertices has minimal
degree $\geq c n$, with known exceptions. Strongly regular graphs correspond to
distance-regular graphs of diameter 2. Babai conjectured that Hamming and
Johnson graphs are the only primitive distance-regular graphs of diameter
$d\geq 3$ whose automorphism group has sublinear minimal degree. We confirm
this conjecture for non-geometric primitive distance-regular graphs of bounded
diameter. We also show if the primitivity assumption is removed, then only one
additional family of exceptions arises, the cocktail-party graphs. We settle
the geometric case in a companion paper.

11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex