The connectivity of the block-intersection graphs of designs |
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| Authors: | Donovan R Hare William Mc Cuaig |
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| Institution: | (1) Department of Mathematics and Statistics, Simon Fraser University, V5A 1S6 Burnaby, B.C., Canada;(2) Department of Mathematics and Statistics, University of Victoria, P.O. Box 3045, V8W 3P4 Victoria, B.C., Canada |
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| Abstract: | It is shown that the vertex connectivity of the block-intersection graph of a balanced incomplete block design,BIBD (v, k, 1), is equal to its minimum degree. A similar statement is proved for the edge connectivity of the block-intersection graph of a pairwise balanced design,PBD (v, K, 1). A partial result on the vertex connectivity of these graphs is also given. Minimal vertex and edge cuts for the corresponding graphs are characterized.Research supported in part by a B.C. Science Council G.R.E.A.T. Scholarship.Research supported in part by an NSERC Postdoctoral Fellowship. |
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| Keywords: | block design block-intersection graph graph connectivity |
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