Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Graph extensions, edit number and regular graphs   A graph G on n vertices is said to be extendable if G can be modified to form
a new graph H on more than n vertices, while preserving the degrees of the
vertices common to G and H. The added vertices all have the same degree and we
define edit numbers to quantify the amount of modification needed to obtain the
extended graph. Characterizing graphs with least possible edit numbers, we
obtain that graphs with zero edit number can be extended using regular graphs.
We also describe an iterative algorithm to construct connected regular graphs
on arbitrarily large vertex sets, starting from the complete graph on a fixed
set of vertices.

35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph