#### Date of Publication

12-2019

#### Document Type

Master's Thesis

#### Degree Name

Master of Science in Mathematics

#### Subject Categories

Mathematics

#### College

College of Science

#### Department/Unit

Mathematics and Statistics

#### Thesis Adviser

Francis Joseph H. Campeña

#### Abstract/Summary

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.

#### Abstract Format

html

#### Language

English

#### Format

Electronic

#### Accession Number

CDTG007374

#### Keywords

Rings (Algebra); Graph labelings

#### Upload Full Text

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#### Recommended Citation

Chua, D. E. (2019). On efficient zero ring labeling of some classes of trees. Retrieved from https://animorepository.dlsu.edu.ph/etd_masteral/6297

#### Embargo Period

9-5-2022