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The F-connectivity of a graph. (English) Zbl 0687.05030

The paper introduces a new type of conditional connectivity; F- connectivity of a graph G. This is defined as follows: For F an induced subgraph of G, the F-connectivity of G is the minimum number of vertices whose removal produces the trivial graph or a disconnected graph, each of whose components is a subgraph of F. The F-edge-connectivity of G is defined similarly. Bounds on the F-connectivity of a graph are investigated and a Whitney-type inequality relating F-connectivity and F- edge-connectivity of a graph is established.
Reviewer: R.E.L.Aldred

MSC:

05C40 Connectivity
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