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Sumset Valuations of Graphs and Their Applications

Sumset Valuations of Graphs and Their Applications

Sudev Naduvath, Germina K. Augusthy, Johan Kok
Copyright: © 2020 |Pages: 43
ISBN13: 9781522593805|ISBN10: 1522593802|ISBN13 Softcover: 9781522593812|EISBN13: 9781522593829
DOI: 10.4018/978-1-5225-9380-5.ch009
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MLA

Naduvath, Sudev, et al. "Sumset Valuations of Graphs and Their Applications." Handbook of Research on Advanced Applications of Graph Theory in Modern Society, edited by Madhumangal Pal, et al., IGI Global, 2020, pp. 208-250. https://doi.org/10.4018/978-1-5225-9380-5.ch009

APA

Naduvath, S., Augusthy, G. K., & Kok, J. (2020). Sumset Valuations of Graphs and Their Applications. In M. Pal, S. Samanta, & A. Pal (Eds.), Handbook of Research on Advanced Applications of Graph Theory in Modern Society (pp. 208-250). IGI Global. https://doi.org/10.4018/978-1-5225-9380-5.ch009

Chicago

Naduvath, Sudev, Germina K. Augusthy, and Johan Kok. "Sumset Valuations of Graphs and Their Applications." In Handbook of Research on Advanced Applications of Graph Theory in Modern Society, edited by Madhumangal Pal, Sovan Samanta, and Anita Pal, 208-250. Hershey, PA: IGI Global, 2020. https://doi.org/10.4018/978-1-5225-9380-5.ch009

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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.

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