The Sparing Number of the Cartesian Products of Certain Graphs

Let N0 be the set of all non-negative integers. An integer additive set-indexer (IASI) is defined as 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, where f(u)+f(v) is the sumset of f(u) and f(v) and P(N0) is the power set of N0. If f+(uv) = k ∀ uv ∈ E(G), then f is said to be a k-uniform integer additive set-indexer. An integer additive set-indexer f is said to be a weak integer additive set-indexer if |f+(uv) | = max(|f(u)|, |f(v)|) ∀ uv ∈ E(G). In this paper, we study about the sparing number of the cartesian product of two graphs. Key Words: Integer additive set-indexers, mono-indexed elements of a graphs, weak integer additive set-indexers, sparing number of a graph. AMS Subject Classification: 05C78