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An improved upper bound for the bondage number of graphs on surfaces

✍ Scribed by Jia Huang


Book ID
113567699
Publisher
Elsevier Science
Year
2012
Tongue
English
Weight
209 KB
Volume
312
Category
Article
ISSN
0012-365X

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Bounds on the bondage number of a graph
✍ Bert L. Hartnell; Douglas F. Rall πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 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

An upper bound for the path number of a
✍ Alan Donald πŸ“‚ Article πŸ“… 1980 πŸ› John Wiley and Sons 🌐 English βš– 529 KB

## Abstract The path number of a graph __G__, denoted __p(G)__, is the minimum number of edge‐disjoint paths covering the edges of __G.__ LovΓ‘sz has proved that if __G__ has __u__ odd vertices and __g__ even vertices, then __p(G)__ ≀ 1/2 __u__ + __g__ ‐ 1 ≀ __n__ ‐ 1, where __n__ is the total numbe