IRMA-International.org: Creator of Knowledge
Information Resources Management Association
Advancing the Concepts & Practices of Information Resources Management in Modern Organizations

Sumset Valuations of Graphs and Their Applications

Sumset Valuations of Graphs and Their Applications
View Sample PDF
Author(s): Sudev Naduvath (Christ University, India), Germina K. Augusthy (Central University of Kerala, India) and Johan Kok (Tshwane Metropolitan Police Department, South Africa)
Copyright: 2020
Pages: 43
Source title: Handbook of Research on Advanced Applications of Graph Theory in Modern Society
Source Author(s)/Editor(s): Madhumangal Pal (Vidyasagar University, India), Sovan Samanta (Tamralipta Mahavidyalaya, India) and Anita Pal (National Institute of Technology Durgapur, India)
DOI: 10.4018/978-1-5225-9380-5.ch009

Purchase

View Sumset Valuations of Graphs and Their Applications on the publisher's website for pricing and purchasing information.

Abstract

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{sumset labelling} 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.

Related Content

Arunaben Prahladbhai Gurjar, Shitalben Bhagubhai Patel. © 2022. 30 pages.
Meghna Babubhai Patel, Jagruti N. Patel, Upasana M. Bhilota. © 2022. 10 pages.
Vo Ngoc Phu, Vo Thi Ngoc Tran. © 2022. 27 pages.
Steven Walczak. © 2022. 17 pages.
Priyanka P. Patel, Amit R. Thakkar. © 2022. 26 pages.
Vo Ngoc Phu, Vo Thi Ngoc Tran. © 2022. 34 pages.
Sarat Chandra Nayak, Subhranginee Das, Bijan Bihari Misra. © 2022. 20 pages.
Body Bottom