Date of Award


Degree Name

Doctor of Philosophy



First Advisor

Dr. Arthur T. White

Second Advisor

Dr. Joseph Buckley

Third Advisor

Dr. Linda Kraai

Fourth Advisor

Dr. Gary Chartrand


The genus of a design (BIBD or PBIBD) is defined to be the genus of its corresponding hypergraph (objects as vertices, blocks as edges); that is, the genus of the bipartite graph associated with the hypergraph in a natural way. The Euler formula is used to establish a lower bound (gamma) for the genus of a block design. An imbedding of the design of the surface of genus (gamma) is then described by a voltage hypergraph or voltage graph. Use of the lower bound formula leads to a characterization of planar BIBDs. A connection between a block design derived from a graph imbedding and the hypergraph imbedding of the design is established. This leads to the determination of genus formulas for several infinite families of designs. The concept of the generalized pseudocharacteristic of a design is developed along with formulas for infinite families of designs.

Access Setting

Dissertation-Open Access

Included in

Mathematics Commons