The isoperimetric problem in block designs
AuthorSurani, Muhammad Adib
AffiliationSchool of Mathematics and Statistics
Document TypePhD thesis
Access StatusOpen Access
© 2018 Dr. Muhammad Adib Surani
This thesis focuses on the problem of determining the isoperimetric numbers of Levi graphs of balanced incomplete block designs. We study two versions of this: the vertex-isoperimetric number and the edge-isoperimetric number. In the general case, we manage to obtain strong upper and lower bounds on these numbers for Levi graphs of arbitrary block designs. We also obtain stronger or even exact values for some families of graphs, particularly those arising from finite geometries or difference sets.
Keywordsisoperimetric number; block designs; Levi graphs
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