A study on prime arithmetic integer additive set-indexers of graphs

Let N₀ be the set of all non-negative integers and P(N₀) be its power set. An integer additive set-indexer (IASI) is defined as an injective function f:V (G) → P(N₀) such that the induced function ƒ+: E (G) → P(N₀) defined by ƒ+(uv) = f(u) + f(v) is also injective, where N₀ 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.