Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Total graph of a signed graph   The total graph is built by joining the graph to its line graph by means of
the incidences. We introduce a similar construction for signed graphs. Under
two similar definitions of the line signed graph, we define the corresponding
total signed graph and we show that it is stable under switching. We consider
balance, the frustration index and frustration number, and the largest
eigenvalue. In the regular case we compute the spectrum of the adjacency matrix
of the total graph and the spectra of certain compositions, and we determine
some with exactly two main eigenvalues.

23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph