Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Projective dimension and regularity of the path ideal of the line graph   By generalizing the notion of the path ideal of a graph, we study some
algebraic properties of some path ideals associated to a line graph. We show
that the quotient ring of these ideals are always sequentially Cohen-Macaulay
and also provide some exact formulas for the projective dimension and the
regularity of these ideals. As some consequences, we give some exact formulas
for the depth of these ideals.

31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio