Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Bounding the Diameter of the Commuting Graph of a Group   The commuting graph of a group $G$ is the simple undirected graph whose
vertices are the non-central elements of $G$ and two distinct vertices are
adjacent if and only if they commute. It is conjectured by Jafarzadeh and
Iranmanesh that there is a universal upper bound on the diameter of the
commuting graphs of finite groups when the commuting graph is connected. In
this paper we determine upper bounds on the diameter of the commuting graph for
some classes of groups to rule them out as possible counterexamples to this
conjecture. We also give an example of an infinite family of groups with
trivial centre and diameter 6, the previously largest known diameter for an
infinite family was 5 for $S_n$.

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The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
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The categories of this paper are: eess
18
The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph