Results 31 to 40 of about 121 (97)
Distance signless Laplacian spectral radius and perfect matching in graphs and bipartite graphs
, 2021 The distance matrix $\mathcal{D}$ of a connected graph $G$ is the matrix indexed by the vertices of $G$ which entry $\mathcal{D}_{i,j}$ equals the distance between the vertices $v_i$ and $v_j$. The distance signless Laplacian matrix $\mathcal{Q}(G)$ of graph $G$ is defined as $\mathcal{Q}(G)=Diag(Tr)+\mathcal{D}(G)$, where $Diag(Tr)$ is the diagonal ...
Liu, Chang, Li, Jianping
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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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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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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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Inequalities for Distance Signless Laplacian Matrix Under Minimum-Degree Constraints
Journal of MathematicsFor a connected graph G of order n, let DG denote its distance matrix and let TrG be the diagonal matrix formed by the vertex transmissions. The distance signless Laplacian of G is defined by DQ=DG+TrG.
Mohd Abrar Ul Haq, S. Pirzada, Y. Shang
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New bounds on the distance Laplacian and distance signless Laplacian spectral radii
, 2019 Let G be a simple undirected connected graph. In this paper, new upper bounds on the distance Laplacian spectral radius of G are obtained. Moreover, new lower and upper bounds for the distance signless Laplacian spectral radius of G are derived.
Rojo, Óscar +2 more
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, 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 $Tr(G)$
Panigrahi, Pratima, Atik, Fouzul
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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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Some sharp bounds on the distance signless Laplacian spectral radius of graphs
, 2013 M. Aouchiche and P. Hansen proposed the distance Laplacian and the distance signless Laplacian of a connected graph [Two Laplacians for the distance matrix of a graph, LAA 439 (2013) 21{33]. In this paper, we obtain three theorems on the sharp upper bounds of the spectral radius of a nonnegative matrix, then apply these theorems to signless Laplacian ...
Hong, Wenxi, You, Lihua
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Further results on the distance signless Laplacian spectrum of graphs
, 2018 The distance signless Laplacian matrix [Formula: see text] of a connected graph [Formula: see text] is defined as [Formula: see text], where [Formula: see text] is the distance matrix of [Formula: see text] and [Formula: see text] is the diagonal matrix
Abdollah Alhevaz +2 more
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