### Arithmetic integer additive set-valued graphs: a creative review

#### Abstract

For a non-empty ground set X, finite or infinite, the set-valuation or set-labeling of a given graph G is an injective function f: V(G) → P(X), where P(X) is the power set of the set X. A set-indexer of a graph G is an injective set-valued function f: V(G) → P(X) such that the function f∗ : E(G) → P(X)−{Φ} defined by f∗(uv) = f(u)∗f(v) for every uv∈E(G) is also injective, where ∗ is a binary operation on sets. Let N0 be the set of all non-negative integers and P(N0) is its power set. An integer additive set-labeling (IASL) of a graph G is 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), where f(u) + f(v) is the sumset of the sets f(u) and f(v). An IASL f of a graph G is said to be an integer additive set-indexer (IASI) of G if the induced function f+ is also injective. In this paper, we critically and creatively review the concepts and properties of a particular type integer additive set-valuation, called arithmetic integer additive set-valuation of graphs.

**Published:**2020-04-13

**How to Cite this Article:**N.K. Sudev, K.P. Chithra, K.A. Germina, Arithmetic integer additive set-valued graphs: a creative review, J. Math. Comput. Sci., 10 (2020), 1020-1049 Copyright © 2020 N.K. Sudev, K.P. Chithra, K.A. Germina. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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