Classical conditions for (weakly-)antistrong digraphs

An antidirected trail in a digraph is one where the arcs alternate between moving forward and backward. In particular, an antidirected trail is categorized as a forward antidirected trail if it begins and ends with a forward arc. A digraph D with n vertices (where $n\ge 3$) is termed antistrong if, for any pair of vertices p and q in $V\left(D\right)$, there exists a forward antidirected trail from p to q. Additionally, a digraph D is weakly-antistrong if, for any pair of vertices p and q in $V\left(D\right)$, there exists either a forward-backward antidirected $(p,q)$-trail or a forward antidirected $(p,q)$-trail. In this study, we provide a degree sum condition for digraphs to be (weakly)-antistrong, which is superior to the ore-type condition given by Yuan (2023). We additionally present necessary and sufficient condition for bipartite digraphs to qualify as weakly-antistrong, and necessary and sufficient conditions for transitive digraphs and total digraphs to be antistrong. Furthermore, we give an arc number condition for digraphs to be antistrong.