Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pseudo-distance-regularised graphs are distance-regular or
  distance-biregular   The concept of pseudo-distance-regularity around a vertex of a graph is a
natural generalization, for non-regular graphs, of the standard
distance-regularity around a vertex. In this note, we prove that a
pseudo-distance-regular graph around each of its vertices is either
distance-regular or distance-biregular. By using a combinatorial approach, the
same conclusion was reached by Godsil and Shawe-Taylor for a distance-regular
graph around each of its vertices. Thus, our proof, which is of an algebraic
nature, can also be seen as an alternative demonstration of Godsil and
Shawe-Taylor's theorem.

5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn