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Universal adjacency matrices with two eigenvalues

Haemers,W.H.
; 
Omidi,G.R.
Abstract
Consider a graph Γ on n vertices with adjacency matrix A and degree sequence (d1,…,dn). A universal adjacency matrix of Γ is any matrix in Span {A,D,I,J} with a nonzero coefficient for A, where D=diag(d1,…,dn) and I and J are the n × n identity and all-ones matrix, respectively. Thus a universal adjacency matrix is a common generalization of the adjacency, the Laplacian, the signless Laplacian and the Seidel matrix. We investigate graphs for which some universal adjacency matrix has just two eigenvalues. The regular ones are strongly regular, complete or empty, but several other interesting classes occur.
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Appeared previously as CentER Discussion Paper 2010-119
Date
2011
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Tilburg University Research Output Collection
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Haemers, W H & Omidi, G R 2011, 'Universal adjacency matrices with two eigenvalues', Linear Algebra and its Applications, vol. 435, no. 10, pp. 2520-2529. https://doi.org/10.1016/j.laa.2011.02.023
URI
https://hdl.handle.net/20.500.14602/55539
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