Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Domination Value in Graphs   A set $D \subseteq V(G)$ is a \emph{dominating set} of $G$ if every vertex
not in $D$ is adjacent to at least one vertex in $D$. A dominating set of $G$
of minimum cardinality is called a $\gamma(G)$-set. For each vertex $v \in
V(G)$, we define the \emph{domination value} of $v$ to be the number of
$\gamma(G)$-sets to which $v$ belongs. In this paper, we study some basic
properties of the domination value function, thus initiating \emph{a local
study of domination} in graphs. Further, we characterize domination value for
the Petersen graph, complete $n$-partite graphs, cycles, and paths.

6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga