DOIAbstract
AbstractA graph G is (n, λ)-connected if it satisfies the following conditions: (1) |V(G)|⩾n+1; (2) for any subset S⊆V(G) and any subset L⊆E(G) with λ|S|+|L|<nλ, G−S−L is connected. The (n, λ)-connectivity is a common extension of both the vertex-connectivity and the edge-connectivity. An (n, 1)-connected graph is an n-(vertex)-connected graph, and a (1, λ)-connected graph is a λ-edge-connected graph. An (n, λ)-connected graph G is said to be minimally (n, λ)-connected if for any edge e in E(G), G−e is not (n, λ)-connected. Let G be a minimally (n, λ)-connected graph and let W be the set of its vertices of degree more than nλ. Then we first prove that for any subset W′ of W, the minimum degree of the subgraph of G induced by the vertex set ...
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