On digraphs with polygonal restricted numerical range

In 2020, Cameron et al. introduced the restricted numerical range of a digraph (directed graph) as tool for characterizing digraphs and studying their algebraic connectivity. Notably, with degenerate polygon (that is, point or line segment) were completely described. this article, we extend those results to include whose is non-degenerate convex polygon. general, refer polygonal. We provide computational methods identifying these polygonal show that they can be broken into three disjoint classes: normal, restricted-normal, pseudo-normal digraphs. Sufficient conditions normal are provided, directed join two in restricted-normal digraph. Moreover, prove joins only when order square-free twice number. Finally, construct not all orders neither nor