Abundancy of $z$-\v Solt\'es' digraphs

TL;DR

This paper proves the existence of infinitely many  Solte9s' digraphs, extending the concept from graphs to digraphs, and provides an example with trivial automorphism group, highlighting their structural diversity.

Contribution

It introduces the concept of  Solte9s' digraphs, proves their infinite abundance, and presents an example with trivial automorphism group, advancing the understanding of their properties.

Findings

Existence of infinitely many  Solte9s' digraphs

Construction of a  Solte9s' digraph with trivial automorphism group

Extension of Solte9s' graph concepts to digraphs

Abstract

We prove the existence of infinitely many \v Solt\'es' digraphs, the digraph analogue of \v Solt\'es' graphs. We also give an example of a \v Solt\'es' digraph with trivial automorphism group.