## Abstract Chartrand and Stewart have shown that the line graph of an __n__βconnected graph is itself __n__βconnected. This paper shows that for every pair of integers __m__ > __n__ > 1 there is a graph of point connectivity __n__ whose line graph has point connectivity __m__. The corresponding qu
Cycles in Graphs with Prescribed Stability Number and Connectivity
β Scribed by M. Kouider
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 113 KB
- Volume
- 60
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract We determine the minimum number of edges in a regular connected graph on __n__ vertices, containing a complete subgraph of order __k__ β€ __n__/2. This enables us to confirm and strengthen a conjecture of P. ErdΓΆs on the existence of regular graphs with prescribed chromatic number.
## 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
Let f (n) be the minimum number of cycles present in a 3-connected cubic graph on n vertices. In 1986, C. A. Barefoot, L. Clark, and R. Entringer (Congr. Numer. 53, 1986) showed that f (n) is subexponential and conjectured that f (n) is superpolynomial. We verify this by showing that, for n sufficie
## Abstract A set __S__ of vertices in a graph __G__ is a total dominating set of __G__ if every vertex of __G__ is adjacent to some vertex in __S__. The minimum cardinality of a total dominating set of __G__ is the total domination number Ξ³~t~(__G__) of __G__. It is known [J Graph Theory 35 (2000)
## 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