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PreprintCC BY-NC-ND 4.0HAL

Proof of the Göbel-Veldman conjecture on diametrical graphs

  • Xingzhi Zhan
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Abstract

A graph is called noncircular if it is not a cycle. A nontrivial connected graph G of diameter d is called diametrical if, for every vertex v of G, there exists a unique vertex at distance d from v. In 1986, Göbel and Veldman conjectured that the order of a noncircular diametrical graph of diameter d is at least 4(d -1). We prove this conjecture. Diametrical graphs were called even graphs by Gobel and Veldman.

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Cite

BibTeXRIS
BibTeX
@misc{zhan2026proof,
  title = {{Proof of the Göbel-Veldman conjecture on diametrical graphs}},
  author = {Xingzhi Zhan},
  howpublished = {HAL},
  year = {2026},
  month = aug,
  url = {https://hal.science/hal-05746382v1},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Proof of the Göbel-Veldman conjecture on diametrical graphs
AU  - Xingzhi Zhan
PY  - 2026
DA  - 2026/08/30
PB  - HAL
UR  - https://hal.science/hal-05746382v1
AB  - A graph is called noncircular if it is not a cycle. A nontrivial connected graph G of diameter d is called diametrical if, for every vertex v of G, there exists a unique vertex at distance d from v. In 1986, Göbel and Veldman conjectured that the order of a noncircular diametrical graph of diameter d is at least 4(d -1). We prove this conjecture. Diametrical graphs were called even graphs by Gobel and Veldman.
ER  -