Hak, ArtemHaponenko, VladyslavKozerenko, SergiySerdiuk, Andrii2023-10-062023-10-062023Unique eccentric point graphs and their eccentric digraphs / Artem Hak, Vladyslav Haponenko, Sergiy Kozerenko, Andrii Serdiuk // Discrete Mathematics. - 2023. - Vol. 346, Issue 12. - Article number 113614. - https://doi.org/10.1016/j.disc.2023.1136140012-365Xhttps://doi.org/10.1016/j.disc.2023.113614https://ekmair.ukma.edu.ua/handle/123456789/26330We study graph-theoretic properties of eccentric digraphs of unique eccentric point graphs (shortly, uep-graphs). The latter are the connected graphs in which every vertex has a unique eccentric vertex. In particular, we characterize uep-graphs and the corresponding eccentric digraphs in the following classes: self-centered graphs having the number of vertices twice as diameter, block graphs, and graphs with diameter three. Also, we obtain non-trivial properties of weak components in eccentric digraphs of uep-graphs with diameter four and pose several open questions in this direction.enunique eccentric point grapheccentric digrapheccentricity of a vertexblock grapharticleArticle