Strongly regular graphs with parameters (4m4,2m4+m2,m4+m2,m4+m2) exist for all m1

Authors:
Willem H. Haemers;Qing Xiang
Affiliations:
Department of Econometrics and O.R., Tilburg University, Tilburg, The Netherlands;Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA
Venue:
European Journal of Combinatorics
Year:
2010

Citing 6
Cited 1

Some infinite classes of special Williamson matrices and difference sets

Journal of Combinatorial Theory Series A
Linear codes and the existence of a reversible Hadamard difference set in Z2×Z2×Z45

Journal of Combinatorial Theory Series A
Constructions of Hadamard difference sets

Journal of Combinatorial Theory Series A
A unifying construction for difference sets

Journal of Combinatorial Theory Series A
Regular Article: Maximal Energy Graphs

Advances in Applied Mathematics
On the Existence of Abelian Hadamard Difference Sets and a New Family of Difference Sets

Finite Fields and Their Applications

Divisible design graphs

Journal of Combinatorial Theory Series A

Quantified Score

Hi-index	0.00

Visualization

Abstract

Using results on Hadamard difference sets, we construct regular graphical Hadamard matrices of negative type of order 4m^4 for every positive integer m. If m1, such a Hadamard matrix is equivalent to a strongly regular graph with parameters (4m^4,2m^4+m^2,m^4+m^2,m^4+m^2). Strongly regular graphs with these parameters have been called max energy graphs, because they have maximal energy (as defined by Gutman) among all graphs on 4m^4 vertices. For odd m=3 the strongly regular graphs seem to be new.