Date of Publication

9-3-1994

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

Blessilda Raposa

Defense Panel Chair

Severino Gervacio

Defense Panel Member

Severino Diesto
Arlene Pascasio

Abstract/Summary

The thesis presents four main theorems on cyclic tournaments. The first deals with the problem of determining the size of any equivalence class of a tournament A in the set C(v) of all cyclic tournaments of order v. The form of an element of the set W(v) of all subgroups of S(v) of odd orders containing C = (123...v) as an automorphism group for some cyclic tournaments is introduced by the second proposition. This is extended to the form of a maximal element of W(v) which is demonstrated by the third theorem using the Polya composition operation. The last theorem discusses a way to determine if an element of W(v) is of the largest order by a certain linear order of odd primes.The main results presented by Noboru Ito in the article On Cyclic Tournaments are amplified. Illustrations are provided to lend plausibility to the theorems. Related theorems and definitions needed in the subsequent arguments of the study but are not stated in Ito's paper are also presented.Some of the primary properties of cyclic tournaments are proved in this study. In addition, a procedure to construct a cyclic tournament such that the automorphism group contains an element of W(v) is demonstrated.The thesis presents four main theorems on cyclic tournaments. The first theorem deals with the problem of determining the size of any equivalence class of a tournament A in the set C(v) of all cyclic tournaments of order v. The form of an element of the set W(v) of all subgroups of S(v) of odd orders containing C = (123...v) as an automorphism group for some cyclic tournaments is introduced by the second proposition. This is extended to the form of a maximal element of W(v) which is demonstrated by the third theorem using the Polya composition operation. The last theorem discusses a way to determine if an element of W(v) is of the largest order by a certain linear order of odd primes.

Abstract Format

html

Language

English

Format

Print

Accession Number

TG02248

Shelf Location

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

Physical Description

144 leaves

Keywords

Paths and cycles (Graph theory); Graph theory; Combinatorial group theory; Matrices; Homomorphisms (Mathematics)

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