Unique eccentric point graphs and their eccentric digraphs
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Date
2023
Authors
Hak, Artem
Haponenko, Vladyslav
Kozerenko, Sergiy
Serdiuk, Andrii
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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.
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Keywords
unique eccentric point graph, eccentric digraph, eccentricity of a vertex, block graph, article
Citation
Unique 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.2023.113614