Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The normalized Laplacian and related indexes of graphs with edges blew
  up by cliques   In this paper, we introduce the clique-blew up graph $CL(G)$ of a given graph
$G$, which is obtained from $G$ by replacing each edge of $G$ with a complete
graph $K_n$. We characterize all the normalized Laplacian spectrum of the grpah
$CL(G)$ in term of the given graph $G$. Based on the spectrum obtained, the
formulae to calculate the multiplicative degree-Kirchhoff index, the Kemeny's
constant and the number of spanning trees of $CL(G)$ are derived well. Finally,
the spectrum and indexes of the clique-blew up iterative graphs are present.

12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
1
The categories of this paper are: cs