Results 21 to 30 of about 114 (91)
Variation of sum of two largest eigenvalues of the distance matrices of four-leaf graph
Journal of Hebei University of Science and Technology, 2020 In order to accurately obtain the extremum of the distance eigenvalues of fowr-leaf graphs under tow graph transformations in any case, two graph transformations of four-leaf graphs and the results of the above problems were given by using the properties
Zhe LYU, Yubin GAO
doaj +1 more source
Bounds on the α‐Distance Energy and α‐Distance Estrada Index of Graphs
Discrete Dynamics in Nature and Society, Volume 2020, Issue 1, 2020., 2020 Let G be a simple undirected connected graph, then Dα(G) = αTr(G) + (1 − α)D(G) is called the α‐distance matrix of G, where α ∈ [0,1], D(G) is the distance matrix of G, and Tr(G) is the vertex transmission diagonal matrix of G. In this paper, we study some bounds on the α‐distance energy and α‐distance Estrada index of G.
Yang Yang +3 more
wiley +1 more source
On distance signless Laplacian eigenvalues of zero divisor graph of commutative rings
AIMS Mathematics, 2022 <abstract><p>For a simple connected graph $ G $ of order $ n $, the distance signless Laplacian matrix is defined by $ D^{Q}(G) = D(G) + Tr(G) $, where $ D(G) $ and $ Tr(G) $ is the distance matrix and the diagonal matrix of vertex transmission degrees, respectively. The zero divisor graph $ \Gamma(R) $ of a finite commutative ring $ R $ is
Bilal Ahmad Rather +4 more
openaire +2 more sources
New bounds for the signless Laplacian spread [PDF]
, 2019 © 2018 Elsevier Inc.Let G be an undirected simple graph. The signless Laplacian spread of G is defined as the maximum distance of pairs of its signless Laplacian eigenvalues.
Leal, Laura +3 more
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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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On the multiplicity of Laplacian eigenvalues for unicyclic graphs [PDF]
, 2022 summary:Let $G$ be a connected graph of order $n$ and $U$ a unicyclic graph with the same order. We firstly give a sharp bound for $m_{G}(\mu )$, the multiplicity of a Laplacian eigenvalue $\mu $ of $G$. As a straightforward result, $m_{U}(1)\le n-2$. We
Wen, Fei, Huang, Qiongxiang
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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
wiley +1 more source
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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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
wiley +1 more source
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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