Let /~(G), F(G) and IR(G) be the independence number, the upper domination number and the upper irredundance number, respectively. A graph G is called In this paper, we present a characterization of F-perfect graphs in terms of a family of forbidden induced subgraphs, and show that the class of F-p
Domination and irredundance in cubic graphs
โ Scribed by E.J. Cockayne; C.M. Mynhardt
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 552 KB
- Volume
- 167-168
- Category
- Article
- ISSN
- 0012-365X
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๐ SIMILAR VOLUMES
In a graph G, a set X is called a stable set if any two vertices of X are nonadjacent. A set X is called a dominating set if every vertex of V-X is joined to at least one vertex of X. A set Xis called an irredundant set if every vertex of X, not isolated in X, has at least one proper neighbor, that
The vertices of the queem;' graph {~, are the squares of an n ร n chessboard and two squares are adjacent ifa queen placed on one covers the other. It is shown that the domination num;~'r of Q. is at most 31n/54 + O(1), that Q. possesses minimal dominating sets of cardina~tty 5n/2 -O(l) and that the
In this paper we consider the following parameters: IR(G), the upper irredundance number, which is the order of the largest maximal irredundant set, I'(G), the upper domination number, which is the order of the largest minimal dominating set and /3(G), the independence number, which is the order of
## Abstract A vertex __x__ in a subset __X__ of vertices of an undericted graph is __redundant__ if its closed neighbourhood is contained in the union of closed neighborhoods of vertices of __X__ โ {__x__}. In the context of a communications network, this means that any vertex that may receive comm