The minimum number of edges in a vertex diameter-2-critical graph (Q1356444)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: The minimum number of edges in a vertex diameter-2-critical graph |
scientific article; zbMATH DE number 1018501
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The minimum number of edges in a vertex diameter-2-critical graph |
scientific article; zbMATH DE number 1018501 |
Statements
The minimum number of edges in a vertex diameter-2-critical graph (English)
0 references
9 November 1997
0 references
A graph \(G\) is called vertex diameter-2-critical if \(\text{diam} (G)=2\) and \(\text{diam} (G-x)>2\) for each vertex \(x\) of the graph. The authors prove that such a graph of order \(n\geq 23\) has at least \((5n-17)/2\) edges. The proof is long and complicated. They also show that this bound is attained for infinitely many graphs.
0 references
vertex diameter-2-critical
0 references
