Cospectral mates for the union of some classes in the Johnson association scheme
Cioabă,Sebastian M. Haemers,Willem H. Johnston,Travis McGinnis,Matt
Cioabă,Sebastian M.
Haemers,Willem H.
Johnston,Travis
McGinnis,Matt
Abstract
Let n≥k≥2 be two integers and S a subset of {0,1,…,k−1}. The graph JS(n,k) has as vertices the k-subsets of the n-set [n]={1,…,n} and two k-subsets A and B are adjacent if |A∩B|∈S. In this paper, we use Godsil–McKay switching to prove that for m≥0, k≥max(m+2,3) and S={0,1,…,m}, the graphs JS(3k−2m−1,k) are not determined by spectrum and for m≥2, n≥4m+2 and S={0,1,…,m} the graphs JS(n,2m+1) are not determined by spectrum. We also report some computational searches for Godsil–McKay switching sets in the union of classes in the Johnson scheme for k≤5.
Description
Date
2018-02-15
Journal Title
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Volume Title
Publisher
Research Projects
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Keywords
Determined by spectrum, Eigenvalues, Godsil–McKay switching, Graph, Johnson association scheme, Kneser graph
Citation
Cioabă, S M, Haemers, W H, Johnston, T & McGinnis, M 2018, 'Cospectral mates for the union of some classes in the Johnson association scheme', Linear Algebra and its Applications, vol. 539, pp. 219-228. https://doi.org/10.1016/j.laa.2017.11.011