Bounds on the distance signless Laplacian spectral radius in terms of clique number
TL;DR: In this article, a sharp lower bound as well as a sharp upper bound in terms of the clique number were derived for the distance signless Laplacian spectral radius of a connected graph.
Abstract: The distance signless Laplacian spectral radius of a connected graph , denoted by , is the maximal eigenvalue of the distance signless Laplacian matrix of . In this paper, we find a sharp lower bound as well as a sharp upper bound of in terms of the clique number. Furthermore, both extremal graphs are uniquely determined.
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TL;DR: In this article, the convex combination of convex combinations D α (G ) of D i a g ( T r ) and D ( G ) is studied and the spectral properties of D α(G ) are given and a few open problems are discussed.
42 citations
TL;DR: In this paper, a connected graph with distance matrix D(G) is defined for any α ∈ [0, 1] and the Dα-matrix of G is defined as Dα(G)=αTr(G)+1−α)D(G).
Abstract: Let G be a connected graph with distance matrix D(G), and let Tr(G) be the diagonal matrix of vertex transmissions of G. For any α∈[0,1], the Dα-matrix of G is defined as Dα(G)=αTr(G)+(1−α)D(G). In...
21 citations
Cites background from "Bounds on the distance signless Lap..."
...In [19,26], it was proved that if s ≥ t ≥ 1 then ρα(Guv(s + 1, t − 1)) > ρα(Guv(s, t)) for α = 0, (1)2 ....
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...Lin and Lu [19] determined the graphs withminimum andmaximum distance signless Laplacian spectral radius among connected graphs with fixed order and clique number....
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...For distance signless Laplacianmatrix, Lin andLu [19] proved that ρ1/2(Gv(s + 1, t − 1)) > ρ1/2(Gv(s, t)) if s ≥ t ≥ 1....
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...The kite graph has the maximumdistance (signless Laplacian) spectral radius among connected graphswith fixed clique number [19,30]....
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TL;DR: In this paper, the authors characterized all graphs with ∂ n (G ) = n − 2 and ∂ 2 ( G ) ∈ [n − 2, n ] when n ≥ 11.
19 citations
TL;DR: In this paper, the effect of graft transformations to decrease and/or increase the distance signless Laplacian spectral radius of a connected graph has been studied, and the authors determined the unique trees with second and third maximum distance signedless logarithm spectral radius, respectively, among trees with given maximum degree.
16 citations
TL;DR: This paper determines the unique graph with minimum distance spectral radius in G n, k D and gives sharp upper and lower bounds for the distance signless Laplacian spectral radius of strongly connected digraphs.
16 citations
References
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01 Jan 2013
TL;DR: The Third Lecture as discussed by the authors discusses the applications of the Zarankiewicz problem and Moore's bound to graph spanners, and the Girth Problem for trees and the Turán problem for trees.
Abstract: 3 Third Lecture 11 3.1 Applications of the Zarankiewicz Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2 The Turán Problem for Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.3 The Girth Problem and Moore’s Bound . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.4 Application of Moore’s Bound to Graph Spanners . . . . . . . . . . . . . . . . . . . . . . . 14
284 citations
"Bounds on the distance signless Lap..." refers background in this paper
...The following lemma is known as Turán’s theorem (see [15])....
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TL;DR: In this article, a distance Laplacian and a signless signless L 1 for the distance matrix of a connected graph is introduced, called the distance L 1 and distance L 2, respectively.
186 citations
"Bounds on the distance signless Lap..." refers background in this paper
...Recently, Aouchiche and Hansen [11] introduced the Laplacian and signless Laplacian for the distance matrix of a connected graph....
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01 Dec 2011
TL;DR: In this paper, a distance Laplacian and a signless signless L 1 for the distance matrix of a connected graph is introduced, called the distance L 1 and distance L 2, respectively.
Abstract: We introduce a Laplacian and a signless Laplacian for the distance matrix of a connected graph, called the distance Laplacian and distance signless Laplacian , respectively. We show the equivalence between the distance signless Laplacian, distance Laplacian and the distance spectra for the class of transmission regular graphs. There is also an equivalence between the Laplacian spectrum and the distance Laplacian spectrum of any connected graph of diameter 2. Similarities between n , as a distance Laplacian eigenvalue, and the algebraic connectivity are established.
131 citations
TL;DR: In this paper, the volumetric overall mass transfer coefficient (KGav) for CO2 absorption into aqueous solutions of 2-amino-2-methyl-1-propanol (AMP) was investigated with an absorption column packed with laboratory structured packings.
Abstract: The volumetric overall mass transfer coefficient (KGav) for CO2 absorption into aqueous solutions of 2-amino-2-methyl-1-propanol (AMP) was investigated with an absorption column packed with laboratory structured packings. The KGav value was evaluated over ranges of main operating variables; that is, up to 10 kPa partial pressure of CO2, 46.2−96.8 kmol/(m2 h) gas molar flux, 6.1−14.6 m3/(m2 h) liquid loading, and 1.1−3.0 kmol/m3 liquid concentration. To allow the mass transfer data to be readily utilized, an empirical KGav correlation for this system was developed. The values of mass transfer coefficient for the CO2−AMP system using a random and the tested structured packings are also compared. For a given system and operating conditions, the structured packing provides, in general, more than eightfold higher overall KGav values compared with those of commercial random packings.
119 citations