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Graphs and Digraphs : Edge-Connectivity

If G is a graph of order n>=2 such that for all distinct nonadjacent vertices u and v,

d(u)+d(v)>=n-1,
then the edge-connectivity k1(G)=Deta(G), where Deta(G) is the least degree of G.

Solution Preview

Proof. We use a theorem in the book: Graphs and Digraphs--G.Chartrand and L.Lesniak.

Theorem: If G is a ...

Solution Summary

An edge-connectivity proof is provided.

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