Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the distance spectra of graphs   The distance matrix of a graph $G$ is the matrix containing the pairwise
distances between vertices. The distance eigenvalues of $G$ are the eigenvalues
of its distance matrix and they form the distance spectrum of $G$. We determine
the distance spectra of halved cubes, double odd graphs, and Doob graphs,
completing the determination of distance spectra of distance regular graphs
having exactly one positive distance eigenvalue. We characterize strongly
regular graphs having more positive than negative distance eigenvalues. We give
examples of graphs with few distinct distance eigenvalues but lacking
regularity properties. We also determine the determinant and inertia of the
distance matrices of lollipop and barbell graphs.

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The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th