Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Note on the Sparing Number of the Sieve Graphs of Certain Graphs   Let $\mathbb{N}_0$ denote the set of all non-negative integers and
$\mathcal{P}(\mathbb{N}_0)$ be its power set. An integer additive set-indexer
(IASI) of a given graph $G$ is an injective function $f:V(G)\to
\mathcal{P}(\mathbb{N}_0)$ such that the induced function $f^+:E(G) \to
\mathcal{P}(\mathbb{N}_0)$ defined by $f^+ (uv) = f(u)+ f(v)$ is also
injective. An IASI $f$ of a graph $G$ is said to be a weak IASI of $G$ if
$|f^+(uv)|=\max(|f(u)|,|f(v)|)$ for all $u,v\in V(G)$. A graph which admits a
weak IASI may be called a weak IASI graph. The sparing number of a graph $G$ is
the minimum number of edges with singleton set-labels required for a graph $G$
to admit a weak IASI. In this paper, we introduce the notion of $k$-sieve
graphs of a given graph and study their sparing numbers.

28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int