Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pebbling on Graph Products and other Binary Graph Constructions   Pebbling on graphs is a two-player game which involves repeatedly moving a
pebble from one vertex to another by removing another pebble from the first
vertex. The pebbling number $\pi(G)$ is the least number of pebbles required so
that, regardless of the initial configuration of pebbles, a pebble can reach
any vertex. Graham conjectured that the pebbling number for the cartesian
product, $G \hspace{1mm}\square\hspace{1mm} H$, is bounded above by $\pi(G)
\pi(H)$. We show that $\pi(G\hspace{1mm}\square\hspace{1mm} H) \le 2\pi(G)
\pi(H)$ and, more sharply, that $\pi(G \hspace{1mm}\square\hspace{1mm} H) \le
(\pi(G)+|G|) \pi(H)$. Furthermore, we provide similar results for other graph
products and graph operations.

29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
1
The categories of this paper are: cs