Results 41 to 50 of about 114 (91)
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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Spectra of products of digraphs
, 2020 A unified approach to the determination of eigenvalues and eigenvectors of specific matrices associated with directed graphs is presented. Matrices studied include the new distance matrix, with natural extensions to the distance Laplacian and distance ...
Ciardo, Lorenzo +3 more
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Distance matrices on the H-join of graphs: A general result and applications [PDF]
, 2018 Given a graph $H$ with vertices $1,\ldots ,s$ and a set of pairwise vertex disjoint graphs $G_{1},\ldots ,G_{s},$ the vertex $i$ of $H$ is assigned to $G_{i}.$ Let $G$ be the graph obtained from the graphs $G_{1},\ldots ,G_{s}$ and the edges connecting ...
Rojo, Oscar +2 more
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Distance Spectra of Some Double Join Operations of Graphs
International Journal of Mathematics and Mathematical Sciences, Volume 2024, Issue 1, 2024.In literature, several types of join operations of two graphs based on subdivision graph, Q‐graph, R‐graph, and total graph have been introduced, and their spectral properties have been studied. In this paper, we introduce a new double join operation based on (H1, H2)‐merged subdivision graph.
B. J. Manjunatha +4 more
wiley +1 more source
More results on the distance (signless) Laplacian eigenvalues of graphs
, 2017 Let $G$ be a connected graph with vertex set $V(G)$ and edge set $E(G)$. Let $Tr(G)$ be the diagonal matrix of vertex transmissions of $G$ and $D(G)$ be the distance matrix of $G$. The distance Laplacian matrix of $G$ is defined as $\mathcal{L}(G)=Tr(G)-D(G)$. The distance signless Laplacian matrix of $G$ is defined as $\mathcal{Q}(G)=Tr(G)+D(G)$.
Xue, Jie +3 more
openaire +2 more sources
Proof of conjectures on the distance signless Laplacian eigenvalues of graphs
Linear Algebra and its Applications, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +2 more sources
On Generalized Distance Gaussian Estrada Index of Graphs [PDF]
, 2019 For a simple undirected connected graph G of order n, let D(G) , DL(G) , DQ(G) and Tr(G) be, respectively, the distance matrix, the distance Laplacian matrix, the distance signless Laplacian matrix and the diagonal matrix of the vertex transmissions of G.
Abdollah Alhevaz +5 more
core +1 more source
On the bounds of Laplacian eigenvalues of $k$-connected graphs [PDF]
, 2015 summary:Let $\mu _{n-1}(G)$ be the algebraic connectivity, and let $\mu _{1}(G)$ be the Laplacian spectral radius of a $k$-connected graph $G$ with $n$ vertices and $m$ edges. In this paper, we prove that \begin {equation*} \mu _{n-1}(G)\geq \frac {2nk^2}
Chen, Xiaodan, Hou, Yaoping
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The spread of generalized reciprocal distance matrix
, 2022 The generalized reciprocal distance matrix $RD_{\alpha}(G)$ was defined as $RD_{\alpha}(G)=\alpha RT(G)+(1-\alpha)RD(G),\quad 0\leq \alpha \leq 1.$ Let $\lambda_{1}(RD_{\alpha}(G))\geq \lambda_{2}(RD_{\alpha}(G))\geq \cdots \geq \lambda_{n}(RD_{\alpha}(G)
Huang, Yufei, Liu, Hechao
core
Spectral characterization of some weighted rooted graphs with cliques
, 2010 The level of a vertex in a rooted graph is one more than its distance from the root vertex. A generalized Bethe tree is a rooted tree in which vertices at the same level have the same degree.
Medina, Luis +3 more
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