The Sparing Number of the Cartesian Products of Certain Graphs

Abstract

Let ${\mathbb{N}}_0$ be the set of all non-negative integers. 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 $|f^{+}(uv)|=max(|f(u)|,|f(v)|)\forall uv\in E(G)$. In this paper, we study about the sparing number of the cartesian product of two graphs.

8 pages, published. arXiv admin note: substantial text overlap with arXiv:1311.0858