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.
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References
J.A. Bondy and U.S.R. Murty,Graph Theory With Applications, Elsevier Science, New York, (1984).
D.R. Hare,The Block-Intersection Graph of Pairwise Balanced Designs, PhD thesis, Simon Fraser University, (1991).
P. Horák and A. Rosa. Decomposing Steiner triple systems into small configurations,Ars Combinatoria, Vol. 26 (1988), pp. 91–105.
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Communicated by S.A. Vanstone
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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Hare, D.R., Mc Cuaig, W. The connectivity of the block-intersection graphs of designs. Des Codes Crypt 3, 5–8 (1993). https://doi.org/10.1007/BF01389350
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DOI: https://doi.org/10.1007/BF01389350