Extremal Singular Graphs

Abstract

A graph is called singular if its adjacency matrix is singular. The problem of characterizing all singular graphs was posed in 1957 by L. Collatz and U. Sinogowitz. Since then, it has been studied intensely due to its great importance in mathematics and in chemistry. However, the problem has proved to be rather complicated and has not yet been solved completely. In this paper, we emphasize on some of the most important results on graphs that are extremal with regard to their nullity/rank. © 2020, Springer Nature Switzerland AG.