Universal adjacency matrices with two eigenvalues

W.H. Haemers, G.R. Omidi

Research output: Contribution to journalArticleScientificpeer-review

27 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)2520-2529
JournalLinear Algebra and its Applications
Issue number10
Publication statusPublished - 2011


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