TY - JOUR
T1 - Universal adjacency matrices with two eigenvalues
AU - Haemers, W.H.
AU - Omidi, G.R.
N1 - Appeared previously as CentER Discussion Paper 2010-119
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
U2 - 10.1016/j.laa.2011.02.023
DO - 10.1016/j.laa.2011.02.023
M3 - Article
SN - 0024-3795
VL - 435
SP - 2520
EP - 2529
JO - Linear Algebra and its Applications
JF - Linear Algebra and its Applications
IS - 10
ER -