Diameter-critical graphs
β Scribed by N. P. Khomenko; N. A. Ostroverkhii
- Book ID
- 112478582
- Publisher
- Springer
- Year
- 1971
- Tongue
- English
- Weight
- 556 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0041-5995
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
A graph is diameter 2-critical if the graph has diameter 2 and the deletion of any edge increases its diameter. We prove that if G is diameter 2-critical graph on n vertices and e edges, then (i) e ~< [14n2 ] for n <~ 24, and (ii) e < !4n2 + (n 2 -16.2 n + 56)/320 (<0.2532 n2), for n/> 25.
## 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
## Abstract A graph is __k__βdominationβcritical if Ξ³(__G) = k__, and for any edge __e__ not in __G__, Ξ³(__G + e) = k__ β 1. In this paper we show that the diameter of a domination __k__βcritical graph with __k__ β§ 2 is at most 2__k__ β 2. We also show that for every __k__ β§ 2, there is a __k__βdom