Weak Integer Additive Set-Indexers of Certain Graph

An integer additive set-indexer is defined as an injective function f: V (G) → 2N0 such that the induced function gf: E(G) → 2N0 defined by gf (uv) = f(u)+f(v) is also injective, where f(u)+f(v) is the sum set of f(u) and f(v) and N0 is the set of all non-negative integers. If gf (uv) = k ∀ uv ∈ E(G), then f is said to be a k-uniform integer additive set-indexers. An integer additive set-indexer f is said to be a weak integer additive set-indexer if |gf (uv) | = max(|f(u)|, |f(v)|) ∀ uv ∈ E(G). We have some characteristics of the graphs which admit weak integer additive set-indexers. In this paper, we study the admissibility of weak integer additive set-indexer by certain finite graph operations. Key words: Integer additive set-indexers, weak integer additive set-indexers, mono-indexed elements of a graph, sparing number of a graph. AMS Subject Classification: 05C78