## Examples of goal-minimally k-diametric graphs for some small values of k

- Ján Plesník
- Australasian J. Combinatorics
- 2008

1 Excerpt

- Published 2002 in Australasian J. Combinatorics

A graph is called vertex diameter critical if its diameter increases when any vertex is removed. Regular vertex diameter critical graphs of every valency k ≥ 2 and diameter d ≥ 2 exist, raising the question of identifying the smallest such graphs. We describe an infinite family of k-regular vertex diameter critical graphs of diameter d with at most kd+ (2k − 3) vertices. This improves the previously known upper bound for all odd valencies k.

@article{Royle2002RegularVD,
title={Regular vertex diameter critical graphs},
author={Gordon F. Royle},
journal={Australasian J. Combinatorics},
year={2002},
volume={26},
pages={209-218}
}