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Sumset Valuations of Graphs and Their Applications

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: 10.4018/9781522593805.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 nonempty sets A and B, denoted by A+B, is defined by A+B=\{a=b: a\inA, b\inB\}. Let X be a nonempty subset of the set \Z and \sP(X) be its power set. An \textit{sumset labelling} of a given graph G is an injective setvalued 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 setlabels 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 sumsetlabeling of given graphs, are also done in this chapter.
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