01-front-cover

Singular and Non-Singular Oriented Wheels

Abstract

This paper extends the concept of singular and non-singular graphs to digraphs. Reduction formulas are established here and used to investigate oriented wheels. All orientations of a wheel which yield a singular digraph are completely determined. Moreover, if an orientation yields a non-singular digraph, the determinant of the adjacency matrix of the oriented wheel is also found.

Singular and Non-Singular Oriented Wheels (236.5 KiB)