On singular and nonsingular digraphs

• Main Author: Jos, Isagani B.
• Format: text
• Language: English
• Published: Animo Repository 2000
• Subjects: Directed graphs; Number theory; Cycles, Algebraic; Mathematics; Number Theory
• Online Access: https://animorepository.dlsu.edu.ph/etd_doctoral/848
• Institution: De La Salle University

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.