TY - JOUR
T1 - Change in vertex status after removal of another vertex in the general setting
AU - Johnson, Charles R.
AU - Saiago, Carlos M.
AU - Toyonaga, Kenji
N1 - info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00297%2F2020/PT#
PY - 2021/3/1
Y1 - 2021/3/1
N2 - In the theory of multiplicities for eigenvalues of symmetric matrices whose graph is a tree, it proved very useful to understand the change in status (Parter, neutral, or downer) of one vertex upon removal of another vertex of given status (both in case the two vertices are adjacent or non-adjacent). As the subject has evolved toward the study of more general matrices, over more general fields, with more general graphs, it is appropriate to resolve the same type of question in the more general settings. “Multiplicity” now means geometric multiplicity. Here, we give a complete resolution in three more general settings and compare these with the classical case (216 “Yes” or “No” results). As a consequence, several unexpected insights are recorded.
AB - In the theory of multiplicities for eigenvalues of symmetric matrices whose graph is a tree, it proved very useful to understand the change in status (Parter, neutral, or downer) of one vertex upon removal of another vertex of given status (both in case the two vertices are adjacent or non-adjacent). As the subject has evolved toward the study of more general matrices, over more general fields, with more general graphs, it is appropriate to resolve the same type of question in the more general settings. “Multiplicity” now means geometric multiplicity. Here, we give a complete resolution in three more general settings and compare these with the classical case (216 “Yes” or “No” results). As a consequence, several unexpected insights are recorded.
KW - Combinatorially symmetric
KW - Eigenvalue
KW - Geometric multiplicity
KW - Graph of a matrix
KW - Tree
UR - http://www.scopus.com/inward/record.url?scp=85097800652&partnerID=8YFLogxK
U2 - 10.1016/j.laa.2020.11.023
DO - 10.1016/j.laa.2020.11.023
M3 - Article
AN - SCOPUS:85097800652
SN - 0024-3795
VL - 612
SP - 128
EP - 145
JO - Linear Algebra and its Applications
JF - Linear Algebra and its Applications
ER -