No Cycling in the Graphs!
โ Scribed by Lowell W. Beineke; Robert C. Vandell
- Book ID
- 104444132
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 257 KB
- Volume
- 11
- Category
- Article
- ISSN
- 1571-0653
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
To a graph G is canonically associated its neighborhood-hypergraph, X(G), formed by the closed neighborhoods of the vertices of G. We characterize the graphs G such that (i) X(G) has no induced cycle, or (ii) #(G) is a balanced hypergraph or (iii) X(G) is triangle free. (i) is another short proof of
We prove the existence of d-regular graphs with arbitrarily large girth and no homomorphism onto the cycle C s , where (d, s)=(3, 9) and (4, 5).
## 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 ฮณ~t~(__G__) of __G__. It is known [J Graph Theory 35 (2000)