Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quintic graphs with every edge in a triangle   We characterise the quintic (i.e. 5-regular) multigraphs with the property
that every edge lies in a triangle. Such a graph is either from a set of small
graphs or is formed by adding a perfect matching to a line graph of a cubic
graph as double edges, or can be reduced by a sequence of operations to one of
these graphs.

16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an