On Certain Arithmetic Integer Additive set-indexers of Graphs

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 (IASI) of a graph $G$ is an injective function $f:V(G)\to $\mathcal{P}$($\mathbb{N}$_0)$suchthattheinducedfunction$f^+:E(G) \to $\mathcal{P}$($\mathbb{N}$_0)$definedby$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 two special types of arithmetic IASIs.