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
On the bondage number of a graph
โ Scribed by Yue-Li Wang
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 162 KB
- Volume
- 159
- Category
- Article
- ISSN
- 0012-365X
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โฆ Synopsis
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).
๐ SIMILAR VOLUMES
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.
We consider the following graph labeling problem, introduced by Leung et al. (3. Y-T. Leung, 0. Vornberger, and J. D. Witthoff, On some variants of the bandwidth minimization problem. SIAM J. Comput. 13 (1984) 650-667). Let G be a graph of order n, and f a bijection from the separation number of G,