A Study on Integer Additive Set-Graceful Graphs

A set-labeling of a graph G is an injective function f: V (G) → P(X), where X is a finite set and a set-indexer of G is a set-labeling such that the induced function f ⊕ : E(G) → P(X) − {∅} defined by f⊕(uv) = f(u)⊕f(v) for every uv∈E(G) is also injective. An integer additive set-labeling is an injective function f: V (G) → P(N0), N0 is the set of all non-negative integers and an integer additive set-indexer is an integer additive set-labeling such that the induced function f+: E(G) → P(N0) defined by f+(uv) = f(u) + f(v) is also injective. In this paper, we extend the concepts of set-graceful labeling to integer additive set-labelings of graphs and provide some results on them. Key words: Set-indexers, integer additive set-indexers, set-graceful graphs, integer additive set-graceful labeling, integer additive set-graceful graphs. AMS Subject Classification: 05C78