Weak integer additive set-labeled graphs: A creative review
Abstract
For a non-empty ground set XX, finite or infinite, the set-valuation or set-labeling of a given graph GG is an injective function f:V(G)→𝒫(X), where 𝒫(X) is the power set of the set X. A set-valuation or a set-labeling of a graph G is an injective set-valued 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) for every uv∈E(G), where ∗ is a binary operation on sets. Let ℕ0 be the set of all non-negative integers and 𝒫(ℕ0) be its power set. An integer additive set-labeling (IASL) is defined as an injective function f:V(G)→𝒫(ℕ0) such that the induced function f+:E(G)→𝒫(ℕ0) is defined by f+(uv)=f(u)+f(v). An IASL f is said to be an integer additive set-indexer if f+ is also injective. A weak IASL is an IASL f such that |f+(uv)|=max(f(u),f(v)). In this paper, critical and creative review of certain studies made on the concepts and properties of weak integer additive set-valued graphs is intended.
Communicated by M.-M. Deza
Dedicated to the memory of Professor Belamannu Devadas Acharya
Remember to check out the Most Cited Articles! |
---|
Check out our Mathematics books for inspirations & up-to-date information in your research area today! |