On certain arithmetic integer additive set-indexers of graphs

Abstract

Let ℕ0 denote the set of all non-negative integers and 𝒫(ℕ0) be its power set. An integer additive set-indexer (IASI) of a graph G is an injective function f : V(G) → 𝒫(ℕ0) such that the induced function f+ : E(G) → 𝒫(ℕ0) defined by f+ (uv) = f(u) + f(v) is also injective. A graph G which admits an IASI is called an integer additive set-indexed graph (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.