 Classical conditions for (weakly-)antistrong digraphsLili Yuan and Jixiang Meng Applied Mathematics and Computation, 2025, vol. 507, issue C Abstract: 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≥3) is termed antistrong if, for any pair of vertices p and q in V(D), 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(D), 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. Keywords: Transitive digraph; Weakly-antistrong; Bi-Cayley digraph; Antistrong (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:507:y:2025:i:c:s0096300325003194 DOI: 10.1016/j.amc.2025.129593 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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