Minimum statuses of connected graphs with fixed maximum degree and order
β Scribed by Chiang Lin, Wei-Han Tsai, Jen-Ling Shang, Yuan-Jen Zhang
- Book ID
- 118801996
- Publisher
- Springer US
- Year
- 2011
- Tongue
- English
- Weight
- 492 KB
- Volume
- 24
- Category
- Article
- ISSN
- 1382-6905
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## Abstract It is well known that certain graphβtheoretic extremal questions play a central role in the study of communication network vulnerability. Herein we consider a generalization of some of the classical results in this area. We define a (__p__, Ξ, Ξ΄, Ξ») graph as a graph having __p__ points,
It was proved by Chartrand f hat if G is a graph of order p for which the minimum degree is at least [&I, then the edge-connectivity of G equals the minimum degree of G. It is shown here that one may allow vertices of degree less than $p and still obtain the same conclusion, provided the degrees are
If a grrrph G hao edge connectivity A then the vertex fiat ha a partition V(a) = U U W ash that 61 esntainti exactly A edgea from U to W, Wen~se if Qo ia a maximal graph of order n and edge connectivity A than C$, is sbtctined from the dkjsint union of two complete oubgragh8, B,[U] and &T,[ Wg, by a