Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distance $r$-domination number and $r$-independence complexes of graphs   For $r\geq 1$, the $r$-independence complex of a graph $G$, denoted
Ind$_r(G)$, is a simplicial complex whose faces are subsets $A \subseteq V(G)$
such that each component of the induced subgraph $G[A]$ has at most $r$
vertices. In this article, we establish a relation between the distance
$r$-domination number of $G$ and (homological) connectivity of Ind$_r(G)$. We
also prove that Ind$_r(G)$, for a chordal graph $G$, is either contractible or
homotopy equivalent to a wedge of spheres. Given a wedge of spheres, we also
provide a construction of a chordal graph whose $r$-independence complex has
the homotopy type of the given wedge.

34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th