Some New Results on Weak Integer Additive Set-Labeling of Graphs

Let N0 denote the set of all non-negative integers and P(N0) be its power set. An integer additive set-labeling (IASL) of a graph G is an injective function f : V (G) → P(N0) such that the induced function f : E(G)→ P(N0) is defined by f(uv) = f(u)+f(v), where f(u)+f(v) is the sumset of f(u) and f(v). An IASL f is said to be an integer additive set-indexer (IASI) if the associated edge-function f is also injective. An IASL f of a given graph G is said to be a weak integer additive set-labeling (WIASL) of G if the cardinality of the set-label of every edge of G is equal to the cardinality of the set-label of at least one end vertex of it. In this paper, we study the admissibility of weak integer additive set-labeling by different graphs.