On isomorphic, nonisomorphic and the number of tournaments from three tournament construction algorithms

Date of Publication

1999

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

Severino V. Gervacio

Defense Panel Chair

Leonor A. Ruivivar

Defense Panel Member

Yvette Lim
Yolando B. Beronque

Abstract/Summary

A tournament T of order n is a digraph V(T), A(T) with vertex-set V(T)=&1,2,...,n such that for every pair of distinct vertices i and j in V(T), (i,j) element A(T) or (j,i) element A(T) but not both. The score Si of a vertex i element V(T) is the number of arcs (i,j) element A(T). In this thesis, it is assumed that the vertices of T are labeled in such a way that S1 is less than or equal to S2 less than or equal to...less than or equal to Sn. The nondecreasing sequence Si1 less than or equal to i less than or equal to n = s1,S2,...,Sn is called the score sequence of T. The sequence di 1 less than or equal to i less than or equal to n=d1,d2...,dn where di = si-i+1 is called its deviation sequence.This study gives sufficient conditions in isomorphic and nonisomorphic tournaments constructed from the three tournament construction algorithms of Gervacio in [6,7]. The number of tournaments with a specified score sequence constructed from each algorithm are also determined.

Abstract Format

html

Language

English

Format

Print

Accession Number

TG02936

Shelf Location

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

Physical Description

91 leaves

Keywords

Graph theory; Algorithms; Isomorphism (Mathematics)

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