Topological Integer Additive Set-Graceful Graphs

Let N0 denote the set of all non-negative integers and X be any subset of X. Also denote the power set of X by P(X). An integer additive set-labeling (IASL) of a graph G is an injective function f : V (G) ! P(X) such that the induced function f+ : E(G) ! P(X) 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 a topological IASL (Top-IASL) if f(V (G)) [ f;g is a topology of the ground set X. An IASL is said to be an integer additive set-graceful labeling (IASGL) if for the induced edgefunction f+, f+(E(G)) = P(X)??f;; f0gg. In this paper, we study certain types of IASL of a given graph G, which is a topological integer additive set-labeling as well as an integer additive set-graceful labeling of G.