Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Graded Betti numbers of some circulant graphs   Let $G$ be the circulant graph $C_n(S)$ with $S \subseteq \{1, 2, \dots,
\lfloor \frac{n}{2} \rfloor\}$, and let $I(G)$ denote the edge ideal in the
polynomial ring $R=\mathbb{K}[x_0, x_1, \dots, x_{n-1}]$ over a field
$\mathbb{K}$. In this paper, we compute the $\mathbb{N}$-graded Betti numbers
of the edge ideals of three families of circulant graphs
$C_n(1,2,\dots,\widehat{j},\dots,\lfloor \frac{n}{2} \rfloor)$,
$C_{lm}(1,2,\dots,\widehat{2l},\dots, \widehat{3l},\dots,\lfloor \frac{lm}{2}
\rfloor)$ and $C_{lm}(1,2,\dots,\widehat{l},\dots,\widehat{2l},\dots,
\widehat{3l},\dots,\lfloor \frac{lm}{2} \rfloor)$. Other algebraic and
combinatorial properties like regularity, projective dimension, induced
matching number and when such graphs are well-covered, Cohen-Macaulay,
Sequentially Cohen-Macaulay, Buchsbaum and $S_2$ are also discussed.

36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
16
The categories of this paper are: stat
3
The categories of this paper are: physics
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The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys