Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vertex-imprimitive symmetric graphs with exactly one edge between any
  two distinct blocks   A graph $\Gamma$ is called $G$-symmetric if it admits $G$ as a group of
automorphisms acting transitively on the set of ordered pairs of adjacent
vertices. We give a classification of $G$-symmetric graphs $\Gamma$ with
$V(\Gamma)$ admitting a nontrivial $G$-invariant partition $\mathcal{B}$ such
that there is exactly one edge of $\Gamma$ between any two distinct blocks of
$\mathcal{B}$. This is achieved by giving a classification of $(G,
2)$-point-transitive and $G$-block-transitive designs $\mathcal{D}$ together
with $G$-orbits $\Omega$ on the flag set of $\mathcal{D}$ such that $G_{\sigma,
L}$ is transitive on $L \setminus \{\sigma\}$ and $L \cap N = \{\sigma\}$ for
distinct $(\sigma, L), (\sigma, N) \in \Omega$, where $G_{\sigma, L}$ is the
setwise stabilizer of $L$ in the stabilizer $G_{\sigma}$ of $\sigma$ in $G$.
Along the way we determine all imprimitive blocks of $G_{\sigma}$ on $V
\setminus \{\sigma\}$ for every $2$-transitive group $G$ on a set $V$, where
$\sigma \in V$.

35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
18
The categories of this paper are: econ