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Weak integer additive set-labeled graphs: A creative review

    https://doi.org/10.1142/S1793557115500527Cited by:1 (Source: Crossref)

    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 uvE(G), where is a binary operation on sets. Let 0 be the set of all non-negative integers and 𝒫(0) be its power set. An integer additive set-labeling (IASL) is defined as an injective function f:V(G)𝒫(0) such that the induced function f+:E(G)𝒫(0) 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

    AMSC: 05C78
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