Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification of 2-extendable bipartite and cubic non-bipartite
  vertex-transitive graphs   In \cite{Chan95}, the authors classified the 2-extendable abelian Cayley
graphs and posed the problem of characterizing all 2-extendable Cayley graphs.
We first show that a connected bipartite Cayley (vertex-transitive) graph is
2-extendable if and only if it is not a cycle. It is known that a non-bipartite
Cayley (vertex-transitive) graph is 2-extendable when it is of minimum degree
at least five \cite{sun}. We next classify all 2-extendable cubic non-bipartite
Cayley graphs and obtain that: a cubic non-bipartite Cayley graph with girth
$g$ is 2-extendable if and only if $g\geq 4$ and it doesn't isomorphic to
$Z_{4n}(1,4n-1,2n)$ or $Z_{4n+2}(2,4n,2n+1)$ with $n\geq 2$. Indeed, we prove a
more stronger result that a cubic non-bipartite vertex-transitive graph with
girth $g$ is 2-extendable if and only if $g\geq 4$ and it doesn't isomorphic to
$Z_{4n}(1,4n-1,2n)$ or $Z_{4n+2}(2,4n,2n+1)$ with $n\geq 2$ or the Petersen
graph.

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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: physics