## Abstract Let __G__ be connected simple graph with diameter __d__(__G__). __G__ is said __v__^+^‐critical if __d__(__G__−__v__) is greater than __d__(__G__) for every vertex __v__ of __G__. Let D′ = max {__d__(__G__−__v__) : __v__ ∈ __V__(__G__)}. Boals et al. [Congressus Numerantium 72 (1990), 1
Minimum vertex-diameter-2-critical graphs
✍ Scribed by Ya-Chen Chen; Zoltán Füredi
- Publisher
- John Wiley and Sons
- Year
- 2005
- Tongue
- English
- Weight
- 182 KB
- Volume
- 50
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
We prove that the minimum number of edges in a vertex‐diameter‐2‐critical graph on n ≥ 23 vertices is (5__n__ − 17)/2 if n is odd, and is (5__n__/2) − 7 if n is even. © 2005 Wiley Periodicals, Inc. J Graph Theory
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