## Abstract Let __G__ be connected simple graph with diameter __d__(__G__). __G__ is said __v__^+^βcritical if __d__(__G__β__v__) is greater than __d__(__G__) for every vertex __v__ of __G__. Let Dβ² = max {__d__(__G__β__v__) : __v__ β __V__(__G__)}. Boals et al. [Congressus Numerantium 72 (1990), 1
On 3--vertex critical graphs of diameter three
β Scribed by Mustapha Chellali; Nader Jafari Rad; Abdollah Khodkar
- Book ID
- 113564695
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 354 KB
- Volume
- 160
- Category
- Article
- ISSN
- 0166-218X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract We prove that the minimum number of edges in a vertexβdiameterβ2βcritical graph on __n__ββ₯β23 vertices is (5__n__βββ17)/2 if __n__ is odd, and is (5__n__/2)βββ7 if __n__ is even. Β© 2005 Wiley Periodicals, Inc. J Graph Theory
A graph is vertex-critical if deleting any vertex increases its diameter. We construct, for each & 5 except &=6, a vertex-critical graph of diameter two on & vertices with at least , where c 2 is some constant. We also construct, for each & 5 except &=6, a vertex-critical graph of diameter two on &