Some New Results on Weak Integer Additive Set-Indexers of Graph Powers

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. An IASI f is said to be a weak IASI if |gf (uv) | = max(|f(u)|, |f(v)|) for all u, v ∈ V (G). A graph which admits a weak IASI may be called a weak IASI graph. The set-indexing number of an element of a graph G, a vertex or an edge, is the cardinality of its set-labels. The sparing number of a graph G is the minimum number of edges with single-ton set-labels, required for a graph G to admit a weak IASI. In this paper, we study the admissibility of weak IASI by certain graph powers and their sparing numbers. Key words: Graph powers, integer additive set-indexers, weak integer additive set-indexers, mono-indexed elements of a graph, sparing number of a graph. AMS Subject Classification: 05C78