(untitled) (Journal of Informatics and Mathematical Sciences, 2018)
Let be the set of all non-negative integers and () be its power set. An integer additive set-indexer (IASI) of a graph G is an injective function f:V(G)→ () such that the induced function f^+:E(G) → () defined by f^+ (uv) = f(u)+ f(v) is also injective. A graph G which admits an IASI is called an IASI-graph. An IASI f is said to be a weak IASI if |f^+(uv)|=(|f(u)|,|f(v)|) and an IASI f is said to be a strong IASI if |f^+(uv)|=|f(u)| |f(v)| for all uvE(G). In this paper, we introduce the notion of arithmetic integer additive set-indexers of a given graph G as an IASI with respect to which all elements of G have arithmetic progressions as their set-labels and study the characteristics of this type of IASIs.