Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear programming bounds for regular graphs   Delsarte, Goethals, and Seidel (1977) used the linear programming method in
order to find bounds for the size of spherical codes endowed with prescribed
inner products between distinct points in the code. In this paper, we develop
the linear programming method to obtain bounds for the number of vertices of
connected regular graphs endowed with given distinct eigenvalues. This method
is proved by some "dual" technique of the spherical case, motivated from the
theory of association scheme. As an application of this bound, we prove that a
connected $k$-regular graph satisfying $g>2d-1$ has the minimum second-largest
eigenvalue of all $k$-regular graphs of the same size, where $d$ is the number
of distinct non-trivial eigenvalues, and $g$ is the girth. The known graphs
satisfying $g>2d-1$ are Moore graphs, incidence graphs of regular generalized
polygons of order $(s,s)$, triangle-free strongly regular graphs, and the odd
graph of degree $4$.

7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex