Divisible design graphs

Authors:
Willem H. Haemers;Hadi Kharaghani;Maaike A. Meulenberg
Affiliations:
Department of Econometrics and Operations Research, Tilburg University, The Netherlands;Department of Mathematics and Computer Science, University of Lethbridge, Canada;Department of Public Health, Erasmus MC, University Medical Center Rotterdam, The Netherlands
Venue:
Journal of Combinatorial Theory Series A
Year:
2011

Citing 6
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Abstract

A divisible design graph is a graph whose adjacency matrix is the incidence matrix of a divisible design. Divisible design graphs are a natural generalization of (v,k,@l)-graphs, and like (v,k,@l)-graphs they make a link between combinatorial design theory and algebraic graph theory. The study of divisible design graphs benefits from, and contributes to, both parts. Using information of the eigenvalues of the adjacency matrix, we obtain necessary conditions for existence. Old results of Bose and Connor on symmetric divisible designs give other conditions and information on the structure. Many constructions are given using various combinatorial structures, such as (v,k,@l)-graphs, distance-regular graphs, symmetric divisible designs, Hadamard matrices, and symmetric balanced generalized weighing matrices. Several divisible design graphs are characterized in terms of the parameters.