Let A(n, k, t) denote the smallest integer e for which every kconnected graph on n vertices can be made (k + t)-connected by adding e new edges. We determine A(n, k, t) for all values of n, k, and t in the case of (directed and undirected) edge-connectivity and also for directed vertex-connectivity
Extremal connectivity and vulnerability in graphs
β Scribed by Lynne L. Doty
- Publisher
- John Wiley and Sons
- Year
- 1989
- Tongue
- English
- Weight
- 290 KB
- Volume
- 19
- Category
- Article
- ISSN
- 0028-3045
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## Abstract An interval graph is said to be extremal if it achieves, among all interval graphs having the same number of vertices and the same clique number, the maximum possible number of edges. We give an intrinsic characterization of extremal interval graphs and derive recurrence relations for t
Let G = ( V , A ) be a digraph with diameter D # 1. For a given integer 2 5 t 5 D , the t-distance connectivity K ( t ) of G is the minimum cardinality of an z --+ y separating set over all the pairs of vertices z, y which are a t distance d(z, y) 2 t. The t-distance edge connectivity X ( t ) of G i