A Study on Prime Arithmetic Integer Additive Set-Indexers of Graphs

Abstract

Let ${\mathbb{N}}_0$ be the set of all non-negative integers and $\mathcal{P}({\mathbb{N}}_0)$ be its power set. 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 ${\mathbb{N}}_0$ is the set of all non-negative integers. A graph $G$ which admits an IASI is called an IASI graph. An IASI of a graph $G$ is said to be an arithmetic IASI if the elements of the set-labels of all vertices and edges of $G$ are in arithmetic progressions. In this paper, we discuss about a particular type of arithmetic IASI called prime arithmetic IASI.

8 pages, submitted. arXiv admin note: text overlap with arXiv:1312.7674, arXiv:1405.6617, arXiv:1403.6435