Further Studies on the Sparing Number of Graphs

Abstract

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 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, where $f(u)+f(v)$ is the sum set of $f(u)$ and $f(v)$. If $f^{+}(uv)=k\forall uv\in E(G)$, then $f$ is said to be a $k$-uniform integer additive set-indexer. An integer additive set-indexer $f$ is said to be a weak integer additive set-indexer if $|f^{+}(uv)|=\max (|f(u)|,|f(v)|)\forall uv\in E(G)$. In this paper, we study the admissibility of weak integer additive set-indexer by certain graphs and graph operations.

10 Pages, Submitted. arXiv admin note: substantial text overlap with arXiv:1310.6091

Cited by in corpus (1)

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