Estimation of the maximum multiplicity of an eigenvalue in terms of the vertex degrees of the graph of a matrix
Charles R. Johnson, Carlos M. Saiago · Electronic Journal of Linear Algebra · 2002
The maximum multiplicity among eigenvalues of matrices with a given graph cannot generally be expressed in terms of the degrees of the vertices (even when the graph is a tree).Given are best possible lower and upper bounds, and characterization of the cases of equality in these bounds.A by-product is a sequential algorithm to calculate the exact maximum multiplicity by simple counting. Key words. Eigenvalues,