Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Group With Maximum Undirected Edges in Directed Power Graph Among All
  Finite Non-Cyclic Nilpotent Groups   In [Curtin and Pourgholi, A group sum inequality and its application to power
graphs, J. Algebraic Combinatorics, 2014], it is proved that among all directed
power graphs of groups of a given order $ n $, the directed power graph of
cyclic group of order $ n $ has the maximum number of undirected edges. In this
paper, we continue their work and we determine a non-cyclic nilpotent group of
an odd order $ n $ whose directed power graph has the maximum number of
undirected edges among all non-cyclic nilpotent groups of order $n$.
  We next determine non-cyclic $p$-groups whose undirected power graphs have
the maximum number of edges among all groups of the same order.

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The categories of this paper are: cs
30
The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th