On Disjunctive and Conjunctive Set-Labelings of Graphs

Abstract : Let X be a non-empty set and P(X) be its power set. A set-valuation or a set-labeling of a given graph G is an injective function f : V (G) → P(X) such that the induced function f * : E(G) → P(X) defined by f * (uv) = f (u) * f (v), where * is a binary operation on sets. A set-indexer 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 also injective. In this paper, two types of set-labelings, called conjunctive set-labeling and disjunctive set-labeling, of graphs are introduced and some properties and characteristics of these types of set-labelings of graphs are studied.
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Sudev Naduvath. On Disjunctive and Conjunctive Set-Labelings of Graphs. Southeast Asian Bulletin of Mathematics, Springer Verlag, 2019. ⟨hal-02263301⟩

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