Sumset valuations of graphs and their applications

Title

Sumset valuations of graphs and their applications

Creator

Naduvath S.; Augusthy G.K.; Kok J.

Description

Graph labelling is an assignment of labels to the vertices and/or edges of a graph with respect to certain restrictions and in accordance with certain predefined rules. The sumset of two non-empty sets A and B, denoted by A+B, is defined by A+B=\(a=b: a\inA, b\inB\). Let X be a non-empty subset of the set \Z and \sP(X) be its power set. An \textit of a given graph G is an injective set-valued function f: V(G)\to\sP_0(X), which induces a function f+: E(G)\to\sP_0(X) defined by f+(uv)=f(u)+f(v), where f(u)+f(v) is the sumset of the set-labels of the vertices u and v. This chapter discusses different types of sumset labeling of graphs and their structural characterizations. The properties and characterizations of certain hypergraphs and signed graphs, which are induced by the sumset-labeling of given graphs, are also done in this chapter. 2020, IGI Global.

Source

Handbook of Research on Advanced Applications of Graph Theory in Modern Society, pp. 208-250.

Date

2019-01-01

Publisher

IGI Global

Coverage

Naduvath S., Department of Mathematics, Christ University, Bangalore, India; Augusthy G.K., Department of Mathematics, Central University of Kerala, Karsargod, Kerala, India; Kok J., Tshwane Metropolitan Police Department, South Africa

Rights

All Open Access; Green Open Access

Relation

ISBN: 978-152259382-9; 1522593802; 978-179980929-6

Format

Online

Language

English

Type

Book chapter

Identifier

https://doi.org/10.4018/978-1-5225-9380-5.ch009

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