Corpus ID: 76649055

# Weak Integer Additive Set-Indexers of Certain Graph Operations

@article{Sudev2013WeakIA,
title={Weak Integer Additive Set-Indexers of Certain Graph Operations},
author={Naduvath Sudev and K. A. Germina},
journal={arXiv: Combinatorics},
year={2013}
}
• Published 23 October 2013
• Mathematics
• arXiv: Combinatorics
An integer additive set-indexer is defined as an injective function $f:V(G)\rightarrow 2^{\mathbb{N}_0}$ such that the induced function $g_f:E(G) \rightarrow 2^{\mathbb{N}_0}$ defined by $g_f (uv) = f(u)+ f(v)$ is also injective, where $f(u)+f(v)$ is the sum set of $f(u)$ and $f(v)$ and $\mathbb{N}_0$ is the set of all non-negative integers. If $g_f(uv)=k \forall uv\in E(G)$, then $f$ is said to be a $k$-uniform integer additive set-indexers. An integer additive set-indexer $f$ is said to be a… Expand
8 Citations
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For a non-empty ground set $X$, finite or infinite, the {\em set-valuation} or {\em set-labeling} of a given graph $G$ is an injective function $f:V(G) \to \mathcal{P}(X)$, where $\mathcal{P}(X)$ isExpand
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• 2014
Abstract Let ℕ0 denote the set of all non-negative integers and P (ℕ0) be its power set. An integer additive set-indexer (IASI) of a graph G is an injective function f : V (G) → P (ℕ0) such that theExpand
The sparing number of certain graph powers
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• Acta Universitatis Sapientiae, Mathematica
• 2019
Abstract Let ℕ0 be the set of all non-negative integers and 𝒫(ℕ0) be its power set. Then, an integer additive set-indexer (IASI) of a given graph G is an injective function f : V(G) → P(ℕ0) suchExpand
Some New Results on Weak Integer Additive Set-Indexers of Graph Powers
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• 2014
An integer additive set-indexer is defined as an injective function $f:V(G)\rightarrow 2^{\mathbb{N}_0}$ such that the induced function $g_f:E(G) \rightarrow 2^{\mathbb{N}_0}$ defined by \$g_f (uv) =Expand

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An integer additive set-indexer is defined as an injective function f : V(G) → 2 N0 such that the induced function gf : E(G) → 2 N0 defined by gf(uv) = f(u)+ f(v) is also injective. An integerExpand
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