An extended eigenvalue-free interval for the eccentricity matrix of threshold graphs

We show that the eigenvalue-free interval for the eccentricity matrix of every threshold graph can be extended from ( - 2 , - 1 ) , as shown in [Z. Qiu, Z. Tang, On the eccentricity spectra of threshold graphs. Discrete Appl. Math. 310 , 75–85 (2022)], to ( - 1 - 2 , - 2 ) ∪ ( - 2 , - 1 ) , and to a...

Full description

Saved in:
Bibliographic Details
Published in:Journal of applied mathematics & computing 2023-02, Vol.69 (1), p.491-503
Main Authors: Anđelić, Milica, Fonseca, Carlos M. da, Koledin, Tamara, Stanić, Zoran
Format: Article
Language:English
Subjects:
Applied mathematics
Computational Mathematics and Numerical Analysis
Eccentricity
Eigenvalues
Graphs
Mathematical and Computational Engineering
Mathematics
Mathematics and Statistics
Mathematics of Computing
Original Research
Theory of Computation
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We show that the eigenvalue-free interval for the eccentricity matrix of every threshold graph can be extended from ( - 2 , - 1 ) , as shown in [Z. Qiu, Z. Tang, On the eccentricity spectra of threshold graphs. Discrete Appl. Math. 310 , 75–85 (2022)], to ( - 1 - 2 , - 2 ) ∪ ( - 2 , - 1 ) , and to a larger interval if we exclude certain pathological cases. Our results are based on the fact that the characteristic matrix of the quotient matrix of the eccentricity matrix of a threshold graph is row equivalent to a particular tridiagonal matrix.
ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-022-01758-3