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 $p and still obtain the same conclusion, provided the degrees are
Minimum degree, edge-connectivity and radius
✍ Scribed by Baoyindureng Wu, Xinhui An, Guojie Liu…
- Book ID
- 120694147
- Publisher
- Springer US
- Year
- 2012
- Tongue
- English
- Weight
- 317 KB
- Volume
- 26
- Category
- Article
- ISSN
- 1382-6905
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If a grrrph G hao edge connectivity A then the vertex fiat ha a partition V(a) = U U W ash that 61 esntainti exactly A edgea from U to W, Wen~se if Qo ia a maximal graph of order n and edge connectivity A than C$, is sbtctined from the dkjsint union of two complete oubgragh8, B,[U] and &T,[ Wg, by a
## Abstract Using the well‐known Theorem of Turán, we present in this paper degree sequence conditions for the equality of edge‐connectivity and minimum degree, depending on the clique number of a graph. Different examples will show that these conditions are best possible and independent of all the