On the sum of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" id="d1e19" altimg="si19.gif"><mml:mi>k</mml:mi></mml:math> largest distance eigenvalues of graphs

Lin, Huiqiu

doi:10.1016/j.dam.2018.12.031

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2024

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Cited by 10 publications

(2 citation statements)

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“…If s = 3 and n = 8, then λ 1 (D(S 8,3 )) = 5 + √ 15 and q(5 + √ 15) < 0, so λ 1 (D(S 8,3 )) < θ (8). If s = 4 and n = 10, then λ 1 (D(S 10,4 )) = 11 and q(11) < 0, so λ 1 (D(S 10,4 )) < θ (10). So Claim 5 holds.…”

Section: Proofsmentioning

confidence: 99%

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Perfect matching and distance spectral radius in graphs and bipartite graphs

Zhang¹,

Lin²

2021

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A perfect matching in a graph G is a set of nonadjacent edges covering every vertex of G. Motivated by recent progress on the relations between the eigenvalues and the matching number of a graph, in this paper, we aim to present a distance spectral radius condition to guarantee the existence of a perfect matching. Let G be an n-vertex connected graph where n is even and λ 1 (D(G)) be the distance spectral radius of G. Then the following statements are true.n−2 by attaching two pendent vertices to a vertex in the n-vertex part.

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Section: Proofsmentioning

confidence: 99%

“…Since then, the study of distance eigenvalues of a graph has become a research subject of enormous interest and this topic has received growing attention over recent years, some latest results see [1,10,11,13,17]. For more results on the distance matrix and its spectral properties, we refer the reader to the excellent survey [2].…”

Section: Introductionmentioning

confidence: 99%