Results 1 to 10 of about 105 (84)
Remoteness and distance, distance (signless) Laplacian eigenvalues of a graph [PDF]
Journal of Inequalities and Applications, 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 $\partial_{1}^{L}\geq\cdots\geq\partial_{n}^{L}$
Huicai Jia, Hongye Song
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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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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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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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Merging the Spectral Theories of Distance Estrada and Distance Signless Laplacian Estrada Indices of Graphs [PDF]
Mathematics, 2019 Suppose that G is a simple undirected connected graph. Denote by D ( G ) the distance matrix of G and by T r ( G ) the diagonal matrix of the vertex transmissions in G, and let α ∈ [ 0 , 1 ] .
Abdollah Alhevaz +2 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.
Ligong Wang
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The Electronic Journal of Linear Algebra, 2018 The \emph{distance matrix} of a simple connected graph $G$ is $D(G)=(d_{ij})$, where $d_{ij}$ is the distance between the $i$th and $j$th vertices of $G$. The \emph{distance signless Laplacian matrix} of the graph $G$ is $D_Q(G)=D(G)+Tr(G)$, where $Tr(G)$ is a diagonal matrix whose $i$th diagonal entry is the transmission of the vertex $i$ in $G$.
Atik, Fouzul, Panigrahi, Pratima
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On the Sum of the Powers of Distance Signless Laplacian Eigenvalues of Graphs
Indian Journal of Pure and Applied Mathematics, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
S Pirzada +2 more
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On the eigenvalues of the distance signless Laplacian matrix of graphs
Proyecciones (Antofagasta)Let G be a connected graph and let DQ(G) be the distance signless Laplacian matrix of G with eigenvalues ρ1≥ ρ2≥…≥ ρn. The spread of the matrix DQ}(G) is defined as s(DQ(G)) := maxi,j| ρi-ρj| = ρ1- ρn. We derive new bounds for the distance signless Laplacian spectral radius ρ1 of G.
Akbar Jahanbani +3 more
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Spectral Properties of the Harary Signless Laplacian and Harary Incidence Energy
MathematicsLet X be a partitioned matrix and let B its equitable quotient matrix. Consider a simple, undirected, connected graph G of order n. In this paper, we employ a technique based on quotient matrices derived from block-partitioned structures to establish new
Luis Medina +2 more
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