On the existence of r-regular singular and nonsingular graphs arbitrarily large order

• Main Authors: Barilea, Michael John M., Wee, Dominique T.
• Format: text
• Language: English
• Published: Animo Repository 2000
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16995
• Institution: De La Salle University

This thesis is based on two articles on singular graphs: Regular Singular and Nonsingular Graphs of Arbitrarily Large Order Exist by Dr. Estrelita Agpalza and Dr. Severino Gervacio and Construction of r-Regular Singular Graphs by Dr. Severino Gervacio and Dr. Leonor Aquino-Ruivivar. The study gave an exposition of the said articles and sought to produce a self-contained write-up on the subject matter included in these articles. The article by Dr. Gervacio and Dr. Agpalza gave a theoretical proof of the existence of singular and nonsingular graphs of arbitrarily large order and discussed the construction of such graphs using process of the cycle graphs. The second article gave a constructive proof of the existence of connected r-regular singular graphs using neighbor sets and I-factors.