TY - JOUR
T1 - ON THE GERŠGORIN DISKS OF DISTANCE MATRICES OF GRAPHS
AU - Aouchiche, Mustapha
AU - Rather, Bilal A.
AU - El Hallaoui, Issmail
N1 - Publisher Copyright:
© 2021, International Linear Algebra Society. All rights reserved.
PY - 2021/1/9
Y1 - 2021/1/9
N2 - For a simple connected graph G, let D(G), T r(G), DL (G) = T r(G) − D(G), and DQ (G) = T r(G) + D(G) be the distance matrix, the diagonal matrix of the vertex transmissions, the distance Laplacian matrix, and the distance signless Laplacian matrix of G, respectively. Atik and Panigrahi [2] suggested the study of the problem: Whether all eigenvalues, except the spectral radius, of D(G) and DQ (G) lie in the smallest Geršgorin disk? In this paper, we provide a negative answer by constructing an infinite family of counterexamples.
AB - For a simple connected graph G, let D(G), T r(G), DL (G) = T r(G) − D(G), and DQ (G) = T r(G) + D(G) be the distance matrix, the diagonal matrix of the vertex transmissions, the distance Laplacian matrix, and the distance signless Laplacian matrix of G, respectively. Atik and Panigrahi [2] suggested the study of the problem: Whether all eigenvalues, except the spectral radius, of D(G) and DQ (G) lie in the smallest Geršgorin disk? In this paper, we provide a negative answer by constructing an infinite family of counterexamples.
KW - Distance Laplacian
KW - Distance matrix
KW - Distance signless Laplacian
KW - Eigenvalues inequalities
KW - Geršgorin disks
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U2 - 10.13001/ELA.2021.6489
DO - 10.13001/ELA.2021.6489
M3 - Article
AN - SCOPUS:85123000930
SN - 1537-9582
VL - 37
SP - 709
EP - 717
JO - Electronic Journal of Linear Algebra
JF - Electronic Journal of Linear Algebra
ER -