Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Hopf algebra on subgraphs of a graph   In this paper, we construct a bialgebraic and further a Hopf algebraic
structure on top of subgraphs of a given graph. Further, we give the dual
structure of this Hopf algebraic structure. We study the algebra morphisms
induced by graph homomorphisms, and obtain a covariant functor from a graph
category to an algebra category.

3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th