Results 21 to 30 of about 120 (101)
The distance matrix and its variants for graphs and digraphs
, 2021 The distance matrix $\mathcal{D}(G)$ of a connected graph $G$ is the matrix whose entries are the pairwise distances between vertices. The distance matrix was defined by Graham and Pollak in 1971 in order to study the problem of loop switching in routing
Reinhart, Carolyn
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A sharp upper bound for the spectral radius of a nonnegative matrix and applications [PDF]
, 2016 summary:We obtain a sharp upper bound for the spectral radius of a nonnegative matrix. This result is used to present upper bounds for the adjacency spectral radius, the Laplacian spectral radius, the signless Laplacian spectral radius, the distance ...
Shu, Yujie, Zhang, Xiao-Dong, You, Lihua
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On distance Laplacian energy in terms of graph invariants
, 2023 summary:For a simple connected graph $G$ of order $n$ having distance Laplacian eigenvalues $ \rho ^{L}_{1}\geq \rho ^{L}_{2}\geq \cdots \geq \rho ^{L}_{n}$, the distance Laplacian energy ${\rm DLE} (G)$ is defined as ${\rm DLE} (G)=\sum _{i=1}^{n}|\rho ^
Rather, Bilal A. +3 more
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Resistance Distance and Kirchhoff Index for a Class of Graphs
Mathematical Problems in Engineering, Volume 2018, Issue 1, 2018., 2018 Let G[F, Vk, Hv] be the graph with k pockets, where F is a simple graph of order n ≥ 1, Vk = {v1, v2, …, vk} is a subset of the vertex set of F, Hv is a simple graph of order m ≥ 2, and v is a specified vertex of Hv. Also let G[F, Ek, Huv] be the graph with k edge pockets, where F is a simple graph of order n ≥ 2, Ek = {e1, e2, …ek} is a subset of the ...
WanJun Yin +3 more
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Generalized Characteristic Polynomials of Join Graphs and Their Applications
Discrete Dynamics in Nature and Society, Volume 2017, Issue 1, 2017., 2017 The Kirchhoff index of G is the sum of resistance distances between all pairs of vertices of G in electrical networks. LEL(G) is the Laplacian‐Energy‐Like Invariant of G in chemistry. In this paper, we define two classes of join graphs: the subdivision‐vertex‐vertex join G1⊚G2 and the subdivision‐edge‐edge join G1⊝G2.
Pengli Lu +3 more
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Bounds on the Spectral Radius of a Nonnegative Matrix and Its Applications
Journal of Applied Mathematics, Volume 2016, Issue 1, 2016., 2016 We obtain the sharp bounds for the spectral radius of a nonnegative matrix and then obtain some known results or new results by applying these bounds to a graph or a digraph and revise and improve two known results.
Danping Huang, Lihua You, Ali R. Ashrafi
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, 2018 The distance signless Laplacian spectral radius of a connected graph [Formula: see text] is the largest eigenvalue of the distance signless Laplacian matrix of [Formula: see text], defined as [Formula: see text], where [Formula: see text] is the distance
Abdollah Alhevaz +2 more
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The Least Algebraic Connectivity of Graphs
Discrete Dynamics in Nature and Society, Volume 2015, Issue 1, 2015., 2015 The algebraic connectivity of a graph is defined as the second smallest eigenvalue of the Laplacian matrix of the graph, which is a parameter to measure how well a graph is connected. In this paper, we present two unique graphs whose algebraic connectivity attain the minimum among all graphs whose complements are trees, but not stars, and among all ...
Guisheng Jiang +3 more
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The Largest Laplacian Spectral Radius of Unicyclic Graphs with Fixed Diameter
Journal of Applied Mathematics, Volume 2013, Issue 1, 2013., 2013 We identify graphs with the maximal Laplacian spectral radius among all unicyclic graphs with n vertices and diameter d.
Haixia Zhang, Baolin Wang
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On the Geršgorin disks of distance matrices of graphs
, 2021 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 $
Rather, Bilal A. +2 more
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