On Weak Integer Additive Set-Indexers of Certain Graph Classes

Abstract

An integer additive set-indexer is defined as an injective function $f:V(G)\to 2^{{\mathbb{N}}_0}$ such that the induced function $g_f:E(G)\to 2^{{\mathbb{N}}_0}$ defined by $g_f(uv)=f(u)+f(v)$ is also injective. An integer additive set-indexer is said to be $k$-uniform if $|g_f(uv)|=k$ for all $u,v\in V(G)$. An integer additive set-indexer $f$ is said to be a weak IASI if $|g_f(uv)|=max(|f(u)|,|f(v)|)$ for all $u,v\in V(G)$. The sparing number of a graph $G$ is the minimum number of edges in $G$ with singleton set-labels, so that $G$ admits a weak integer additive set-indexer. In this paper, we study the admissibility of weak integer additive set-indexers by certain graph classes and certain associated graphs of given graphs.

12 pages, submitted, Journal of Discrete Mathematical Sciences & Cryptography, 2014

References in corpus (1)

• On Weakly Uniform Integer Additive Set-Indexers of Graphs