Motivated by parallel routing in networks with faults, we study the following graph theoretical problem. Let G be a graph of minimum vertex degree d. We say that G is strongly Menger-connected if for any copy G f of G with at most d -2 nodes removed, every pair of nodes u and v in G f are connected
Increasing the connectivity of the star graphs
β Scribed by Eddie Cheng; Marc J. Lipman
- Publisher
- John Wiley and Sons
- Year
- 2002
- Tongue
- English
- Weight
- 104 KB
- Volume
- 40
- Category
- Article
- ISSN
- 0028-3045
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
In this work, we prove that ΞΊ 2 (S n ) = 6(n -3) for n β₯ 4, where S n is the n-dimensional star graph.
We prove that partitionable graphs are 2w -2-connected, that this bound is sharp, and prove some structural properties of cutsets of cardinality 2w -2. The proof of the connectivity result is a simple linear algebraic proof.
The acyclic orientation graph, AO(G), of an undirected graph, G, is the graph whose vertices are the acyclic orientations of G and whose edges are the pairs of orientations differing only by the reversal of one edge. Edelman (1984) has observed that it follows from results on polytopes that when G i