## Abstract We consider finite, undirected, and simple graphs __G__ of order __n__(__G__) and minimum degree Ξ΄(__G__). The connectivity ΞΊ(__G__) for a connected graph __G__ is defined as the minimum cardinality over all vertexβcuts. If ΞΊ(__G__)β<βΞ΄(__G__), then Topp and Volkmann 7 showed in 1993 f
Graphs with given connectivity and independence number or networks with given measures of vulnerability and survivability
β Scribed by Amin, A.; Hakimi, S.
- Book ID
- 114614531
- Publisher
- Institute of Electrical and Electronics Engineers
- Year
- 1973
- Tongue
- English
- Weight
- 1017 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0018-9324
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract For a vertex __v__ of a graph __G__, we denote by __d__(__v__) the __degree__ of __v__. The __local connectivity__ ΞΊ(__u, v__) of two vertices __u__ and __v__ in a graph __G__ is the maximum number of internally disjoint __u__ β__v__ paths in __G__, and the __connectivity__ of __G__ is
## Abstract G. Ringel conjectured that for every positive integer __n__ other than 2, 4, 5, 8, 9, and 16, there exists a nonseparable graph with __n__ cycles. It is proved here that the conjecture is true even with the restriction to planar and hamiltonian graphs.
The interval number of a graph G, denoted i(G), is the least positive integer t such that G is the intersection graph of sets, each of which is the union of t compact real intervals. It is known that every planar graph has interval number at most 3 and that this result is best possible. We investiga