Strongly Regular Graphs and Designs with Three IntersectionNumbers

Authors:
Yury J. Ionin;M. S. Shrikhande
Affiliations:
Department of Mathematics, Central Michigan University, Mt. Pleasant, MI 48859, USA;Department of Mathematics, Central Michigan University, Mt. Pleasant, MI 48859, USA
Venue:
Designs, Codes and Cryptography
Year:
2000

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Abstract

We investigate BIBDs with three intersection numbers,x, y, and z, such that the relation on the block set given byA\sim B iff the cardinality of the intersectionof A and B is not equal to x is an equivalence relation. Withsuch a design, we associate a family of strongly regular graphswith the same parameters. Two constructions producing infinitefamilies of such designs are given.