Title

On singular and nonsingular digraphs

Date of Publication

2000

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Subject Categories

Mathematics | Number Theory

College

College of Science

Department/Unit

Mathematics and Statistics Department

Abstract/Summary

Given a digraph D of order n, there is an associated square matrix of order n called its adjacency matrix. If this adjacency matrix is singular, then D is singular, otherwise D is nonsingular. This study investigates the singularity and nonsingularity of digraphs and in particular of some classes of oriented graphs. It starts with the classification of oriented graphs whose underlying graphs are some well known classes of graphs. These are the paths, cycles, fans, wheels, the complete graph and the complete bipartite graphs. This study also defines some classes of digraphs which are r-regular, asymmetric and circulant. This study also extends certain binary operations on graphs to digraphs. The operations included in this study are the sum, cartesian product, complementation, composition and conjunction. In particular, this study investigates the cartesian product of oriented cycles and paths and that of a circuit and an arbitrary graph, the complement of the digraphs which are r-regular, asymmetric and circulant and the composition and conjunction of cycles and of a special class of oriented cycles, the circuit.

Abstract Format

html

Language

English

Format

Print

Accession Number

TG03093

Shelf Location

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

Physical Description

92 leaves ; Conmputer print-out

Keywords

Directed graphs; Number theory; Cycles, Algebraic

This document is currently not available here.

Share

COinS