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 $p and still obtain the same conclusion, provided the degrees are
Order of a Graph with given Vertex and Edge Connectivity and Minimum Degree
β Scribed by Mohit Singh; Amitabha Tripathi
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 120 KB
- Volume
- 15
- Category
- Article
- ISSN
- 1571-0653
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
If a grrrph G hao edge connectivity A then the vertex fiat ha a partition V(a) = U U W ash that 61 esntainti exactly A edgea from U to W, Wen~se if Qo ia a maximal graph of order n and edge connectivity A than C$, is sbtctined from the dkjsint union of two complete oubgragh8, B,[U] and &T,[ Wg, by a
## Abstract Let __G__ be a connected graph of order __p__ β₯ 2, with edgeβconnectivity 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
## 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