A Study on Topological Integer Additive Set-Labeling of Graphs, Electronic

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. Let G be a graph and let X be a non-empty set. A set-indexer f: V (G) → P(X) is called a topological set-labeling of G if f(V (G)) is a topology of X. An integer additive set-labeling is an injective function f: V (G) → P(N0), whose associated function f+: E(G)→ P(N0) is defined by f(uv) = f(u) + f(v), uv ∈ E(G), where N0 is the set of all non-negative integers and P(N0) is its power set. 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 topological set-labeling of graphs to topological integer additive set-labeling of graphs. Key words: Set-labeling of graphs, Integer additive set-labeling of graphs, topo-logical set-labeling of graphs, topological integer additive set-labeling of graphs. AMS Subject Classification: 05C78