Towards a theory of domination in graphs
β Scribed by Dr. E. J. Cockayne; Dr. S. T. Hedetniemi
- Publisher
- John Wiley and Sons
- Year
- 1977
- Tongue
- English
- Weight
- 666 KB
- Volume
- 7
- Category
- Article
- ISSN
- 0028-3045
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let u(G) and i(G) be the domination number and independent domination number of a graph G. respectively. Sumner and Moore [8] define a graph G to be domination perfect if y( H) = i( H), for every induced subgraph H of G. In this article, we give a finite forbidden induced subgraph characterization o
## Abstract MacGillivray and Seyffarth (J Graph Theory 22 (1996), 213β229) proved that planar graphs of diameter two have domination number at most three and planar graphs of diameter three have domination number at most ten. They also give examples of planar graphs of diameter four having arbitrar
## 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__ (other than itself). The maximum cardinality of a minimal total dominating set of __G__ is the upper total domination number of __G__, denoted by Ξ~__
Vertices x and y dominate a tournament T if for all vertices z / = x, y, either x beats z or y beats z. Let dom(T ) be the graph on the vertices of T with edges between pairs of vertices that dominate T . We show that dom(T ) is either an odd cycle with possible pendant vertices or a forest of cater
A set S of vertices of a graph G is a total dominating set, if every vertex of V (G) is adjacent to some vertex in S. The total domination number of G, denoted by Ξ³ t (G), is the minimum cardinality of a total dominating set of G. We prove that, if G is a graph of order n with minimum degree at leas