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A bound on the size of a graph with given order and bondage number

โœ 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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๐Ÿ“œ SIMILAR VOLUMES


Bounds on the bondage number of a graph
โœ Bert L. Hartnell; Douglas F. Rall ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 317 KB

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
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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).

Sharp bounds on the order, size, and sta
โœ Pierre Hansen; Maolin Zheng ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 276 KB

## 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

A lower bound on the order of regular gr
โœ C. Balbuena; T. Jiang; Y. Lin; X. Marcote; M. Miller ๐Ÿ“‚ Article ๐Ÿ“… 2007 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 129 KB ๐Ÿ‘ 1 views

## 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), 209โ€“218]. A (ฮด, __g__)โ€cage is a small

A counterexample to a conjecture on the
โœ Ulrich Teschner ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 113 KB

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.