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Set-Valuations of Graphs and Their Applications

Set-Valuations of Graphs and Their Applications

Germina K. Augusthy
Copyright: © 2020 |Pages: 37
ISBN13: 9781522593805|ISBN10: 1522593802|ISBN13 Softcover: 9781522593812|EISBN13: 9781522593829
DOI: 10.4018/978-1-5225-9380-5.ch008
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MLA

Augusthy, Germina K. "Set-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. 171-207. https://doi.org/10.4018/978-1-5225-9380-5.ch008

APA

Augusthy, G. K. (2020). Set-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. 171-207). IGI Global. https://doi.org/10.4018/978-1-5225-9380-5.ch008

Chicago

Augusthy, Germina K. "Set-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, 171-207. Hershey, PA: IGI Global, 2020. https://doi.org/10.4018/978-1-5225-9380-5.ch008

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Abstract

A set-valuation of a graph G=(V,E) assigns to the vertices or edges of G elements of the power set of a given nonempty set X subject to certain conditions. A set-indexer of G is an injective set-valuation f:V(G)→2x such that the induced set-valuation f⊕:E(G)→2X on the edges of G defined by f⊕(uv)=f(u)⊕f(v) ∀uv∈E(G) is also injective, where ⊕ denotes the symmetric difference of the subsets of X. Set-valued graphs such as set-graceful graphs, topological set-graceful graphs, set-sequential graphs, set-magic graphs are discussed. Set-valuations with a metric, associated with each pair of vertices is defined as distance pattern distinguishing (DPD) set of a graph (open-distance pattern distinguishing set of a graph (ODPU)) is ∅≠M⊆V(G) and for each u∈V(G), fM(u)={d(u,v): v ϵ M} be the distance-pattern of u with respect to the marker set M. If fM is injective (uniform) then the set M is a DPD (ODPU) set of G and G is a DPD (ODPU)-graph. This chapter briefly reports the existing results, new challenges, open problems, and conjectures that are abound in this topic.

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