Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetric graphs with 2-arc transitive quotients   A graph $\Ga$ is $G$-symmetric if $\Ga$ admits $G$ as a group of
automorphisms acting transitively on the set of vertices and the set of arcs of
$\Ga$, where an arc is an ordered pair of adjacent vertices. In the case when
$G$ is imprimitive on $V(\Ga)$, namely when $V(\Ga)$ admits a nontrivial
$G$-invariant partition $\BB$, the quotient graph $\Ga_{\BB}$ of $\Ga$ with
respect to $\BB$ is always $G$-symmetric and sometimes even $(G, 2)$-arc
transitive. (A $G$-symmetric graph is $(G, 2)$-arc transitive if $G$ is
transitive on the set of oriented paths of length two.) In this paper we obtain
necessary conditions for $\Ga_{\BB}$ to be $(G, 2)$-arc transitive (regardless
of whether $\Ga$ is $(G, 2)$-arc transitive) in the case when $v-k$ is an odd
prime $p$, where $v$ is the block size of $\BB$ and $k$ is the number of
vertices in a block having neighbours in a fixed adjacent block. These
conditions are given in terms of $v, k$ and two other parameters with respect
to $(\Ga, \BB)$ together with a certain 2-point transitive block design induced
by $(\Ga, \BB)$. We prove further that if $p=3$ or $5$ then these necessary
conditions are essentially sufficient for $\Ga_{\BB}$ to be $(G, 2)$-arc
transitive.

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The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
0
The categories of this paper are: hep-ph