Journal article
Unique Eccentric Point Graphs And Their Eccentric Digraphs
Year:
2023Published in:
Discrete MathematicsUnique eccentric point graph
Eccentric digraph
Eccentricity of a vertex
Block graph
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.