A study on the modular sumset labeling of graphs
Abstract
For a positive integer n, let ℤn be the set of all non-negative integers modulo n and 𝒫(ℤn) be its power set. A modular sumset valuation or a modular sumset labeling of a given graph G is an injective function f:V(G)→𝒫(ℤn) such that the induced function f+:E(G)→𝒫(ℤn) defined by f+(uv)=f(u)+f(v). A modular sumset indexer of a graph G is an injective modular sumset valued function f:V(G)→𝒫(ℤn) such that the induced function f+:E(G)→𝒫(ℤn) is also injective. In this paper, some properties and characteristics of this type of modular sumset labeling of graphs are being studied.
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