A Characterisation of Weak Integer Additive Set-Indexers of Graphs

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 $|g_f(e)|=k$ for all $e\in E(G)$. An integer additive set-indexer $f$ is said to be a weak integer additive set-indexer if $|g_f(uv)|=max(|f(u)|,|f(v)|)$ for all $u,v\in V(G)$. In this paper, we study the characteristics of certain graphs and graph classes which admit weak integer additive set-indexers.

12pages, 4 figures, arXiv admin note: text overlap with arXiv:1311.0858

References in corpus (1)

• On Weakly Uniform Integer Additive Set-Indexers of Graphs

Cited by in corpus (12)

• On Integer Additive Set-Indexers of Graphs
• A Note on the Sparing Number of Graphs
• Weak Integer Additive Set-Indexers of Certain Graph Operations
• A Study on the Nourishing Number of Graphs and Graph Powers
• Further Studies on the Sparing Number of Graphs
• On the Sparing Number of the Edge-Corona of Graphs
• Weak Integer Additive Set-Indexers of Certain Graph Products
• A Study on the Sparing Number of the Corona of Certain Graphs
• The Sparing Number of the Cartesian Products of Certain Graphs
• Weak Set-Labeling Number of Certain IASL-Graphs
• A Note on the Sparing Number of the Sieve Graphs of Certain Graphs
• A Note on Sparing Number Algorithm of Graphs