A Study on Topological Integer Additive Set-Labeling of Graphs

Original · EN

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.