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Order of a Graph with given Vertex and Edge Connectivity and Minimum Degree

✍ Scribed by Mohit Singh; Amitabha Tripathi


Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
120 KB
Volume
15
Category
Article
ISSN
1571-0653

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πŸ“œ SIMILAR VOLUMES


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

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## Abstract Let __G__ be a connected graph of order __p__ β‰₯ 2, with edge‐connectivity ΞΊ~1~(__G__) and minimum degree Ξ΄(__G__). It is shown her ethat in order to obtain the equality ΞΊ~1~(__G__) = Ξ΄(__G__), it is sufficient that, for each vertex __x__ of minimum degree in __G__, the vertices in the n

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## Abstract For each pair __s,t__ of natural numbers there exist natural numbers __f(s,t)__ and __g(s,t)__ such that the vertex set of each graph of connectivity at least __f(s,t)__ (respectively minimum degree at least __g(s,t))__ has a decomposition into sets which induce subgraphs of connectivit