1. Unique eccentric point graphs and their eccentric digraphs.
- Author
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Hak, Artem, Haponenko, Vladyslav, Kozerenko, Sergiy, and Serdiuk, Andrii
- Subjects
- *
OPEN-ended questions , *GRAPH connectivity - Abstract
We 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. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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