Determinants of adjacency matrices of some graphs

Authors

Francis Joseph H. Campena, De La Salle University, Manila
Severino V. Gervacio, De La Salle University, Manila

College

College of Science

Department/Unit

Mathematics and Statistics Department

Document Type

Conference Proceeding

Source Title

7th De La Salle University-Osaka University Science Research Workshop

Publication Date

8-2006

Abstract

The adjacency matrix of a graph G having vertices x₁, x₂,...,x_n is the n x n matrix A(G)m= [a_ij] where a_ij = 1 if x_i is adjacent to x_j and x_ij = 0 otherwise. We say that a graph is singular if its adjacency matrix is singular; otherwise we say that it is non-singular. Formulas for the determinant of some types of graphs such as combs, crowns, sparks, and the star paths are shown in this paper and thus determining when these graphs are singular.

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Recommended Citation

Campena, F. H., & Gervacio, S. V. (2006). Determinants of adjacency matrices of some graphs. 7th De La Salle University-Osaka University Science Research Workshop Retrieved from https://animorepository.dlsu.edu.ph/faculty_research/13457

Disciplines

Mathematics

Keywords

Graph theory; Matrices

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