On Certain Types of Product Set-Labeling of Graphs

Abstract : The product set of two sets A and B of integers, denoted by A * B, is the set A * B = {ab : a ∈ A, b ∈ B}. For X ⊆ N, a product set-labeling (PS-labeling) of a graph G is an injective function ƒ : V (G) → P(X) such that the induced function f* : V (G) → P(X) is defined as ƒ*(uv) = ƒ(u) * ƒ(v)≤ uv ∈ E(G), ƒ(u) * ƒ(v) being the product set of ƒ(u) and ƒ(v). The PS-labeling of a graph can be classified into certain types in two ways: in accordance with the cardinalities of the set-labels and according to the nature of the collection of set-labels of elements of the graph G. This paper discusses different types of PS-labeling of graphs.
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Sudev Naduvath. On Certain Types of Product Set-Labeling of Graphs. Journal of Combinatorics, Information & System Sciences, Delhi: Forum for Interdisciplinary Mathematics, 2018. ⟨hal-02263306⟩

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