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 in-teger 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)) ∪ {∅} is a topology of the ground set X. An IASL is said to be an inte-ger additive set-graceful labeling (IASGL) if for the induced edge-function f+, f+(E(G)) = P(X)−{∅, {0}}. In this paper, we study certain types of IASL of a given graph G, which is a topo-logical integer additive set-labeling as well as an integer additive set-graceful labeling of G. Keywords Integer additive set-labeled graphs, integer additive set-graceful graphs, topological integer additive set-labeled graph, topological integer additive set-graceful labeling of graphs. AMS Subject Classification: 05C78 1