Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Graphs determined by signless Laplacian spectra   In the past decades, graphs that are determined by their spectrum have
received more attention, since they have been applied to several fields, such
as randomized algorithms, combinatorial optimization problems and machine
learning. An important part of spectral graph theory is devoted to determining
whether given graphs or classes of graphs are determined by their spectra or
not. So, finding and introducing any class of graphs which are determined by
their spectra can be an interesting and important problem. A graph is said to
be DQS if there is no other non-isomorphic graph with the same signless
Laplacian spectrum. For a DQS graph G, we show that G[rK1 [sK2 is DQS under
certain conditions, where r, s are natural numbers and K1 and K2 denote the
complete graphs on one vertex and two vertices, respectively. Applying these
results, some DQS graphs with independent edges and isolated vertices are
obtained

29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci