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The minimum restricted edge-connected graph and the minimum size of graphs with a given edge–degree

✍ Scribed by Yang, Weihua; Tian, Yingzhi; Li, Hengzhe; Li, Hao; Guo, Xiaofeng

Book ID
122154162
Publisher
Elsevier Science
Year
2014
Tongue
English
Weight
419 KB
Volume
167
Category
Article
ISSN
0166-218X

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On graphs with equal edge-connectivity a
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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

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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