The bondage number b(G) of a graph G is the minimum cardinality of a set of edges of G whose removal from G makes the domination number of G increase. There are several papers discussed the upper bound of b(G). In this paper, we shall give an improved upper bound of b(G).
The bondage number of a graph
β Scribed by John Frederick Fink; Michael S. Jacobson; Lael F. Kinch; John Roberts
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 654 KB
- Volume
- 86
- Category
- Article
- ISSN
- 0012-365X
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π SIMILAR VOLUMES
The bondage number b(G) of a graph G is the minimum cardinality of a set of edges of G whose removal from G results in a graph with domination number larger than that of G. Several new sharp upper bounds for b(G) are established. In addition, we present an infinite class of graphs each of whose bond
The bondage number h(G) of a nonempty graph G was first introduced by Fink, Jacobson, Kinch and Roberts in [3]. They generalized a former approach to domination-critical graphs, In their publication they conjectured that b(G)<d(G)+ 1 for any nonempty graph G.
A set of points S of a graph is convex if any geodesic joining two points of S lies entirely within S. The convex hull of a set T of points is the smallest convex set that contains T. The hull number (h) of a graph is the cardinality of the smallest set of points whose convex hull is the entire grap
## Abstract We study a generalization of the notion of the chromatic number of a graph in which the colors assigned to adjacent vertices are required to be, in a certain sense, far apart. Β© 1993 John Wiley & Sons, Inc.