2014/07/31 by N. K. Sudev, K. A. Germina
Mathematics · #math.CO #msc:05C78
published as ELectronic Journal of Graph Theory and Applications, Vol. 3, Issue.1, 2015, pp. 70-84 · 16 pages, 7 figures, Accepted for publication. arXiv admin note: text overlap with arXiv:1403.3984
arxiv created 2015/03/18 · arxiv updated 2015/03/19
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.