Symmetric even graphs have these properties. For every x there exists a unique antipodal vertex. And all vertices have the same eccentricity the diameter of G.
Refer this article
a survey on eccentric digraph of a (di)graph
medha itagi huilgol
It is hard to answer. With my viewpoints in my paper, Symmetric graphs firstly the potentials of each unit subgraph are equal. And Then n is an even number. While you partition graph with any vertex as the start one, you would obtain a result with same datastructe, which is "symmetric" for low and hight regions. I observe such few cases only.
I will suggest you those links:
A SYMMETRY INDEX FOR GRAPHS
https://www.usukita.org/papers/6081/mowshowitz_dehmer-rev.pdf
Even graphs
http://doc.utwente.nl/70817/1/Gobel86even.pdf
- Badges
- Science topic
- Similar topics
- Mathematical Sciences
- Graphs