G-2021-57
On the Geršgorin discs of distance matrices of graphs
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For a simple connected graph \(G\)
, let \(D(G), ~Tr(G)\)
, \(D^{L}(G)=Tr(G)-D(G)\)
, and \(D^{Q}(G)=Tr(G)+D(G)\)
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 (2018) suggested the study of the problem: Whether all eigenvalues, except the spectral radius, of \(D(G)\)
and \(D^{Q}(G)\)
lie in the smallest Ger\v{s}gorin disc? In this paper, we provide a negative answer by constructing an infinite family of counterexamples.
Published October 2021 , 11 pages
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Publication
Dec 2021
, , and
The Electronic Journal of Linear Algebra, 37, 709–717, 2021
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