Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the normalized Laplacian spectra of some subdivision joins of two
  graphs   For two simple graphs $G_1$ and $G_2$, we denote the subdivision-vertex join
and subdivision-edge join of $G_1$ and $G_2$ by $G_1\dot{\vee}G_2$ and
$G_1\veebar G_2$, respectively. This paper determines the normalized Laplacian
spectra of $G_1\dot{\vee}G_2$ and $G_1\veebar G_2$ in terms of these of $G_1$
and $G_2$ whenever $G_1$ and $G_2$ are regular. As applications, we construct
some non-regular normalized Laplacian cospectral graphs. Besides we also
compute the number of spanning trees and the degree-Kirchhoff index of
$G_1\dot{\vee}G_2$ and $G_1\veebar G_2$ for regular graphs $G_1$ and $G_2$.

12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg