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    Graphs and Digraphs : Edge-Connectivity

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    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.

    © BrainMass Inc. brainmass.com March 4, 2021, 5:44 pm ad1c9bdddf
    https://brainmass.com/math/graphs-and-functions/graphs-digraphs-edge-connectivity-8341

    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

    The expert provides graphs and digraphs for distinct nonadjacent vertices. An edge-connectivity proof is provided.

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