A study of singular and nonsingular graphs using reduction formulas

• Main Authors: Alburo, Gertrude Pauline Gerona, Yen, Li-wen
• Format: text
• Language: English
• Published: Animo Repository 1997
• Subjects: Graph theory; Algebras, Linear; Mathematics > Formulae
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16429
• Institution: De La Salle University

A graph is said to be singular if the determinant of its adjacency matrix is equal to zero. Otherwise, the graph is said to be nonsingular. This thesis studies some classes of graphs in relation to singularity or nonsingularity. Several reduction formulas were used to facilitate the computation of the determinants of adjacency matrices of graphs. Application of the reduction formulas to the computation of determinant of symmetric (0,1)-matrices with zero diagonal is discussed and illustrated. Most of the formulas stated in the theorems in this thesis are results given by Severino Gervacio in his article entitled A Study of Singular Bipartite Graphs and H.M. Rara in her dissertation entitled Singular Graphs. The researchers provided some new results based from the reduction formulas studied.