TY: JOUR
T1 - Ky Fan theorem applied to Randi? energy
A1 - Gutman, Ivan
A1 - Martins, Enide A.
A1 - Robbiano, María
A1 - Martín, Bernardo San
N2 - Let G be a simple undirected graph of order n with vertex set V(G) ={v1, v2, ..., vn}. Let di be the degree of the vertex vi. The Randi? matrix R=(r_{i,j}) of G is the square matrix of order n whose (i, j)-entry is equal to 1/ didj if the vertices vi and vj are adjacent, and zero otherwise. The Randi? energy is the sum of the absolute values of the eigenvalues of R. Let X, Y, and Z be matrices, such that X +Y=Z. Ky Fan established an inequality between the sum of singular values of X, Y, and Z. We apply this inequality to obtain bounds on Randi? energy. We also present results pertaining to the energy of a symmetric partitioned matrix, as well as an application to the coalescence of graphs.
UR - https://ria.ua.pt/handle/10773/13484
Y1 - 2014
PB - Elsevier