On Weak Integer Additive Set-Indexers of Certain Graph Classes
N K Sudev, K A Germina · 2016
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 integer additive set-indexer is said to be k-uniform if |gf (uv) | = k for all u, v ∈ V (G). An integer additive set-indexer f is said to be a weak IASI if |gf (uv) | = max(|f(u)|, |f(v)|) for all u, v ∈ V (G). The sparing number of a graph G is the minimum number of edges in G with singleton set-labels, so that G admits a weak integer additive set-indexer. In this paper, we study the admissibility of weak integer additive set-indexers by certain graph classes and certain associated graphs of given graphs. Key Words: Integer additive set-indexers, weak integer additive set- in-dexers, sparing number. AMS Subject CLassification: 05C78 1