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On Certain Arithmetic Integer Additive set-indexers of Graphs (1405.6617v3)
Published 20 May 2014 in math.CO
Abstract: 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 $f:V(G)\to \mathcal{P}(\mathbb{N}_0)$ 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 two special types of arithmetic IASIs.