## Abstract A graph __G__ is domination perfect if for each induced subgraph __H__ of __G__, ฮณ(__H__) = __i__(__H__), where ฮณ and __i__ are a graph's domination number and independent domination number, respectively. Zverovich and Zverovich [3] offered a finite forbidden induced characterization of
On the domination of the products of graphs II: Trees
โ Scribed by Michael S. Jacobson; Lael F. Kinch
- Publisher
- John Wiley and Sons
- Year
- 1986
- Tongue
- English
- Weight
- 377 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
โฆ Synopsis
For a graph G, a subset of vertices D is a dominating set if for each vertex x not in D, x is adjacent to at least one vertex of D. The domination number, y(G), is the order of the smallest such set. An outstanding conjecture in the theory of domination is for any two graph G and H,
๐ SIMILAR VOLUMES
Let 3:; denote the set of simple graphs with n vertices and m edges, t ( G ) the number of spanning trees of a graph G , and F 2 H if t(K,\E(F))?t(K,\E(H)) for every s? max{u(F), u ( H ) } . We give a complete characterization of >-maximal (maximum) graphs in 3:; subject to m 5 n . This result conta
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
## Abstract Zip product was recently used in a note establishing the crossing number of the Cartesian product __K__~1~,__n__ โก __P__~m~. In this article, we further investigate the relations of this graph operation with the crossing numbers of graphs. First, we use a refining of the embedding metho