A Study on the Sparing Number of the Corona of Certain Graphs

Abstract

An integer additive set-indexer (IASI) is defined as 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 sumset of $f(u)$ and $f(v)$ and $\mathcal{P}({\mathbb{N}}_0)$ is the power set of ${\mathbb{N}}_0$. 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 $|f^{+}(uv)|=max(|f(u)|,|f(v)|)\forall uv\in E(G)$. We have some characteristics of the graphs which admit weak integer additive set-indexers. In this paper, we study about the sparing number of the corona of two graphs.

12 pages, submitted. arXiv admin note: substantial text overlap with arXiv:1311.0858, arXiv:1407.4869, arXiv:1310.6091

Cited by in corpus (1)

• On the Sparing Number of the Edge-Corona of Graphs