Mengerian Results For Distance-\(n\) Connectivity

In the definition of local connectivity, the neighbourhood of a vertex consists of the induced subgraph of all vertices at distance one from the vertex. In {[2]}, we introduced the concept of distance-\(n\) connectivity in which the distance-\(n\) neighbourhood of a vertex consists of the induced subgraph of all vertices at distance less or equal to \(n\) from that vertex. In this paper we present Menger-type results for graphs whose distance-\(n\) neighbourhoods are all \(k\)-connected, \(n \geq 1\).