Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Growth of graph powers   For a graph G, its rth power is constructed by placing an edge between two
vertices if they are within distance r of each other. In this note we study the
amount of edges added to a graph by taking its rth power. In particular we
obtain that either the rth power is complete or "many" new edges are added.
This is an extension of a result obtained by P. Hegarty for cubes of graphs.

7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics