×

Cospectral mates for generalized Johnson and Grassmann graphs. (English) Zbl 1525.05106

Summary: We provide three infinite families of graphs in the Johnson and Grassmann schemes that are not uniquely determined by their spectrum. We do so by constructing graphs that are cospectral but non-isomorphic to these graphs.

MSC:

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
15A18 Eigenvalues, singular values, and eigenvectors
05C75 Structural characterization of families of graphs

Citations:

Zbl 1377.05108

References:

[1] Abiad, A.; Haemers, W. H., Cospectral graphs and regular orthogonal matrices of level 2, Electron. J. Comb., 19 (2012), #P13 · Zbl 1253.05092
[2] Chang, L., The uniqueness and nonuniqueness of triangular association schemes, Sci. Rec., 3, 604-613 (1959) · Zbl 0089.15102
[3] Cioabă, S. M.; Haemers, W. H.; Johnston, T.; McGinnis, M., Cospectral mates for the union of some classes in the Johnson association scheme, Linear Algebra Appl., 539, 219-228 (2018) · Zbl 1377.05108
[4] van Dam, E. R.; Haemers, W. H.; Koolen, J. H.; Spence, E., Characterizing distance-regularity of graphs by the spectrum, J. Comb. Theory, Ser. A, 113, 1805-1820 (2006) · Zbl 1105.05076
[5] van Dam, E. R.; Koolen, J. H., A new family of distance-regular graphs with unbounded diameter, Invent. Math., 162, 189-193 (2005) · Zbl 1074.05092
[6] Godsil, C. D.; McKay, B. D., Constructing cospectral graphs, Aequ. Math., 25, 257-268 (1982) · Zbl 0527.05051
[7] Haemers, W. H.; Ramezani, F., Graphs cospectral with Kneser graphs, Graphs Comb., 531, 159-164 (2010) · Zbl 1232.05125
[8] Hoffman, A. J., On the uniqueness of the triangular association scheme, Ann. Math. Stat., 31, 492-497 (1960) · Zbl 0091.31504
[9] Huang, T.; Liu, C., Spectral characterization of some generalized Odd graphs, Graphs Comb., 15, 195-209 (1999) · Zbl 0934.05088
[10] Ihringer, F.; Munemasa, A., New strongly regular graphs from finite geometries via switching, Linear Algebra Appl., 580, 464-474 (2019) · Zbl 1423.51005
[11] Qiu, L.; Ji, Y.; Wang, W., On a theorem of Godsil and McKay concerning the construction of cospectral graphs, Linear Algebra Appl., 603, 265-274 (2020) · Zbl 1446.05060
[12] Wang, W.; Qiu, L.; Hu, Y., Cospectral graphs, GM-switching and regular rational orthogonal matrices of level p, Linear Algebra Appl., 563, 154-177 (2019) · Zbl 1405.05108
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.