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
A bound on the size of a graph with given order and bondage number
โ Scribed by Bert L. Hartnell; Douglas F. Rall
- Book ID
- 108316472
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 266 KB
- Volume
- 197-198
- Category
- Article
- ISSN
- 0012-365X
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๐ 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 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).
## Abstract We consider graphs __G = (V,E)__ with order ฯ = |__V__|, size __e__ = |__E__|, and stability number ฮฒ~0~. We collect or determine upper and lower bounds on each of these parameters expressed as functions of the two others. We prove that all these bounds are sharp. ยฉ __1993 by John Wiley
## Abstract The girth pair of a graph gives the length of a shortest odd and a shortest even cycle. The existence of regular graphs with given degree and girth pair was proved by Harary and Kovรกcs [Regular graphs with given girth pair, J Graph Theory 7 (1983), 209โ218]. A (ฮด, __g__)โcage is a small
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.