Elsevier

Discrete Mathematics

Volumes 167–168, 15 April 1997, Pages 35-63
Discrete Mathematics

The minimum number of edges in a vertex diameter-2-critical graph

https://doi.org/10.1016/S0012-365X(96)00215-4Get rights and content
Under an Elsevier user license
open archive

Abstract

A simple connected graph G with diam(G) = d is said to be ‘vertex diameter-d-critical’ if diam(Gx) ⩾ d + 1 for any xV(G). We prove that the number of edges in a vertex diameter-2-critical graph on n vertices with n ⩾ 23 is greater than or equal to (5n − 17)/2.

Cited by (0)