Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large Networks of Diameter Two Based on Cayley Graphs   In this contribution we present a construction of large networks of diameter
two and of order $\frac{1}{2}d^2$ for every degree $d\geq 8$, based on Cayley
graphs with surprisingly simple underlying groups. For several small degrees we
construct Cayley graphs of diameter two and of order greater than $\frac23$ of
Moore bound and we show that Cayley graphs of degrees
$d\in\{16,17,18,23,24,31,\dots,35\}$ constructed in this paper are the largest
currently known vertex-transitive graphs of diameter two.

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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci