Results 1 to 10 of about 80 (69)
Remoteness and distance, distance (signless) Laplacian eigenvalues of a graph. [PDF]
J Inequal Appl, 2018 Let G be a connected graph of order n. The remoteness of G, denoted by ρ, is the maximum average distance from a vertex to all other vertices. Let ∂1≥⋯≥∂n $\partial_{1}\geq\cdots\geq\partial_{n}$, ∂1L≥⋯≥∂nL $\partial_{1}^{L}\geq\cdots\geq\partial_{n}^{L}$
Jia H, Song H.
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Distance signless Laplacian eigenvalues, diameter, and clique number [PDF]
Discrete Mathematics Letters, 2022 Summary: Let \(G\) be a connected graph of ordern. Let \(\operatorname{Diag}(\mathrm{Tr})\) be the diagonal matrix of vertex transmissions and let \(\mathcal{D}(G)\) be the distance matrix of \(G\). The distance signless Laplacian matrix of \(G\) is defined as \(\mathcal{D}^{\mathcal{Q}}(G) =\operatorname{Diag}(\mathrm{Tr}) + \mathcal{D}(G)\) and the ...
Saleem Khan, Shariefuddin Pirzada
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Some inequalities involving the distance signless Laplacian eigenvalues of graphs [PDF]
Transactions on Combinatorics, 2021 Given a simple graph $G$, the distance signlesss Laplacian $D^{Q}(G)=Tr(G)+D(G)$ is the sum of vertex transmissions matrix $Tr(G)$ and distance matrix $D(G)$.
Abdollah Alhevaz +3 more
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On comparison between the distance energies of a connected graph. [PDF]
HeliyonLet G be a simple connected graph of order n having Wiener index W(G). The distance, distance Laplacian and the distance signless Laplacian energies of G are respectively defined asDE(G)=∑i=1n|υiD|,DLE(G)=∑i=1n|υiL−Tr‾|andDSLE(G)=∑i=1n|υiQ−Tr‾|, where ...
Ganie HA, Rather BA, Shang Y.
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Discussiones Mathematicae Graph TheorySummary: For a connected graph \(G\) of order \(n\), let \(\mathcal{D}(G)\) be the distance matrix and \(Tr(G)\) be the diagonal matrix of vertex transmissions of \(G\). The distance signless Laplacian (dsL, for short) matrix of \(G\) is defined as \(\mathcal{D}^Q(G)=Tr(G)+\mathcal{D}(G)\), and the corresponding eigenvalues are the dsL eigenvalues of \(
Shariefuddin Pirzada +2 more
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On the Second-Largest Reciprocal Distance Signless Laplacian Eigenvalue [PDF]
Mathematics, 2021 The signless Laplacian reciprocal distance matrix for a simple connected graph G is defined as RQ(G)=diag(RH(G))+RD(G). Here, RD(G) is the Harary matrix (also called reciprocal distance matrix) while diag(RH(G)) represents the diagonal matrix of the total reciprocal distance vertices.
Maryam Baghipur +3 more
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Distance (signless) Laplacian spectrum of dumbbell graphs [PDF]
Transactions on Combinatorics, 2023 In this paper, we determine the distance Laplacian and distance signless Laplacian spectrum of generalized wheel graphs and a new class of graphs called dumbbell graphs.
Sakthidevi Kaliyaperumal +1 more
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Distance (Signless) Laplacian Eigenvalues of $k$-uniform Hypergraphs
Taiwanese Journal of Mathematics, 2022 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, Xiangxiang, Wang, Ligong
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On Extremal Spectral Radii of Uniform Supertrees with Given Independence Number
Discrete Dynamics in Nature and Society, Volume 2022, Issue 1, 2022., 2022 A supertree is a connected and acyclic hypergraph. Denote by Tm,n,α the set of m‐uniform supertrees of order n with independent number α. Focusing on the spectral radius in Tm,n,α, this present completely determines the hypergraphs with maximum spectral radius among all the supertrees with n vertices and independence number α for [m − 1/mn] ≤ α ≤ n − 1,
Lei Zhang +2 more
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New Bounds for the Generalized Distance Spectral Radius/Energy of Graphs
Mathematical Problems in Engineering, Volume 2022, Issue 1, 2022., 2022 Let G be a simple connected graph with vertex set V(G) = {v1, v2, …, vn} and dvi be the degree of the vertex vi. Let D(G) be the distance matrix and Tr(G) be the diagonal matrix of the vertex transmissions of G. The generalized distance matrix of G is defined as Dα(G) = αTr(G) + (1 − α)D(G), where 0 ≤ α ≤ 1. If λ1, λ2, …, λn are the eigenvalues of Dα(G)
Yuzheng Ma +3 more
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