Arithmetic integer additive set-valued graphs: A creative review

Title

Arithmetic integer additive set-valued graphs: A creative review

Creator

Sudev N.K.; Chithra K.P.; Germina K.A.

Description

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) ? { 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. 2020 the author(s).

Source

Journal of Mathematical and Computational Science, Vol-10, No. 4, pp. 1020-1049.

Date

2020-01-01

Publisher

SCIK Publishing Corporation

Subject

Integer additive set-indexers; Set-indexers; Strong integer additive set-indexers; Weak integer additive set-indexers

Coverage

Sudev N.K., Department of Mathematics, CHRIST (Deemed to be University), Bangalore, Karnataka, India; Chithra K.P., Department of Mathematics, CHRIST (Deemed to be University), Bangalore, Karnataka, India; Germina K.A., Department of Mathematics, Central University of Kerala, Kasaragod, Kerala, India

Rights

All Open Access; Gold Open Access

Relation

ISSN: 19275307

Format

Online

Language

English

Type

Review

Identifier

https://doi.org/10.28919/jmcs/4529

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