On the distinguishing partitions and asymmetric uniform hypergraphs

Date of Publication

2016

Document Type

Bachelor's Thesis

Degree Name

Bachelor of Science in Mathematics with specialization in Business Applications

Subject Categories

Statistics and Probability

College

College of Science

Department/Unit

Mathematics and Statistics

Thesis Adviser

Yvette F. Lim

Abstract/Summary

This study is an exposition of the first three sections of the paper entitled Distinguishing Partitions and Asymmetric Uniform Hypergraphs by Ellingham and Schroeder, which appeared in ARS Mathematica Comtemporanea [7]. We give a thorough discussion of the preliminary concepts, proofs of propositions, theorems, and lemmas found in the paper. We also give a discussion on some important properties of hypergraphs. Further, we determine when a distinguishing partition for some special graphs and asymmetric hypergraphs exists. Also, we provided a lemma which states that there are no asymmetric 2-uniform hypergraphs with edges 1 m 5. Lastly, we present our observation that having exactly one nontrivial automorphism in its automorphism group, a graph with 2-distinguishing coloring has a distinguishing partition if and only if there exists a vertex v 2 V (G) such that 2(v) = v.

Abstract Format

html

Language

English

Format

Electronic

Accession Number

CDTU021082

Shelf Location

Archives, The Learning Commons, 12F, Henry Sy Sr. Hall

Physical Description

1 computer disc ; 4 3/4 in.

Keywords

Hypergraphs; Fuzzy hypergraphs; Graph theory

Embargo Period

5-11-2021

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