On efficient zero ring labeling of some classes of trees

A zero ring is a ring in which the product of any two elements is zero, which is the additive identity. A zero ring labeling of a graph is an assignment of distinct elements of a zero ring to the vertices of the graph such that the sum of the labels of any two adjacent vertices is not the zero eleme...

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Main Author: Chua, Dhenmar E.
Format: text
Language:English
Published: Animo Repository 2019
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Online Access:https://animorepository.dlsu.edu.ph/etd_masteral/6297
https://animorepository.dlsu.edu.ph/context/etd_masteral/article/13377/viewcontent/On_Efficient_Zero_Ring2.pdf
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Institution: De La Salle University
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spelling oai:animorepository.dlsu.edu.ph:etd_masteral-133772022-09-06T02:32:22Z On efficient zero ring labeling of some classes of trees Chua, Dhenmar E. A zero ring is a ring in which the product of any two elements is zero, which is the additive identity. A zero ring labeling of a graph is an assignment of distinct elements of a zero ring to the vertices of the graph such that the sum of the labels of any two adjacent vertices is not the zero element in the ring. Given a zero ring labeling of a graph, if the cardinality of the set of distinct sums obtained from all adjacent vertices is equal to the maximum degree of the graph, then the zero ring labeling is efficient. In this paper, we showed the existence of an efficient zero ring labeling for some classes of trees and their disjoint union. In particular, we showed that an efficient zero ring labeling exists for some families of the following classes of trees: path graphs, star graphs, bistars, centipede graphs, caterpillars, spiders, lobsters, and rooted trees. 2019-12-01T08:00:00Z text application/pdf https://animorepository.dlsu.edu.ph/etd_masteral/6297 https://animorepository.dlsu.edu.ph/context/etd_masteral/article/13377/viewcontent/On_Efficient_Zero_Ring2.pdf Master's Theses English Animo Repository Rings (Algebra) Graph labelings Mathematics
institution De La Salle University
building De La Salle University Library
continent Asia
country Philippines
Philippines
content_provider De La Salle University Library
collection DLSU Institutional Repository
language English
topic Rings (Algebra)
Graph labelings
Mathematics
spellingShingle Rings (Algebra)
Graph labelings
Mathematics
Chua, Dhenmar E.
On efficient zero ring labeling of some classes of trees
description A zero ring is a ring in which the product of any two elements is zero, which is the additive identity. A zero ring labeling of a graph is an assignment of distinct elements of a zero ring to the vertices of the graph such that the sum of the labels of any two adjacent vertices is not the zero element in the ring. Given a zero ring labeling of a graph, if the cardinality of the set of distinct sums obtained from all adjacent vertices is equal to the maximum degree of the graph, then the zero ring labeling is efficient. In this paper, we showed the existence of an efficient zero ring labeling for some classes of trees and their disjoint union. In particular, we showed that an efficient zero ring labeling exists for some families of the following classes of trees: path graphs, star graphs, bistars, centipede graphs, caterpillars, spiders, lobsters, and rooted trees.
format text
author Chua, Dhenmar E.
author_facet Chua, Dhenmar E.
author_sort Chua, Dhenmar E.
title On efficient zero ring labeling of some classes of trees
title_short On efficient zero ring labeling of some classes of trees
title_full On efficient zero ring labeling of some classes of trees
title_fullStr On efficient zero ring labeling of some classes of trees
title_full_unstemmed On efficient zero ring labeling of some classes of trees
title_sort on efficient zero ring labeling of some classes of trees
publisher Animo Repository
publishDate 2019
url https://animorepository.dlsu.edu.ph/etd_masteral/6297
https://animorepository.dlsu.edu.ph/context/etd_masteral/article/13377/viewcontent/On_Efficient_Zero_Ring2.pdf
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