On the Sparing Number of the Edge-Corona of Graphs

Abstract

Let ${\mathbb{N}}_0$ be the set of all non-negative integers and $\mathcal{P}({\mathbb{N}}_0)$ be its the power set. An integer additive set-indexer (IASI) of a graph $G$ 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 $f(v)$. An integer additive set-indexer $f$ is said to be a weak integer additive set-indexer (weak IASI) if $|f^{+}(uv)|=\max (|f(u)|,|f(v)|)\forall uv\in E(G)$. The minimum number of singleton set-labeled edges required for the graph $G$ to admit an IASI is called the sparing number of the graph. In this paper, we discuss the admissibility of weak IASI by a particular type of graph product called the edge corona of two given graphs and determine the sparing number of the edge corona of certain graphs.

10 pages, 1 figure, published. arXiv admin note: text overlap with arXiv:1407.5092

References in corpus (2)

• Further Studies on the Sparing Number of Graphs
• A Study on the Sparing Number of the Corona of Certain Graphs