Results 41 to 50 of about 120 (101)

The distance matrix and its variants for graphs and digraphs

, 2022
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
core  

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, Hogben, Leslie, Catral, Minerva, Reinhart, Carolyn   +3 more
core   +1 more source

Distance signless Laplacian eigenvalues, diameter, and clique number [PDF]

Discrete Mathematics Letters, 2022
Saleem Khan, Shariefuddin Pirzada
doaj   +1 more source

Spectra Of Variants Of Distance Matrices Of Graphs And Digraphs: A Survey

, 2022
Distance matrices of graphs were introduced by Graham and Pollack in 1971 to study a problem in communications. Since then, there has been extensive research on the distance matrices of graphs—a 2014 survey by Aouchiche and Hansen on spectra of distance ...
Hogben, L., Reinhart, Carolyn
core   +1 more source

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, Shang, Yilun, Maryam Baghipur, Baghipur, Maryam, Alhevaz, Abdollah, Yilun Shang   +5 more
core   +1 more source

On the Largest Distance (Signless Laplacian) Eigenvalue of Non-transmission-regular Graphs

, 2018
Let $G=(V(G),E(G))$ be a $k$-connected graph with $n$ vertices and $m$ edges. Let $D(G)$ be the distance matrix of $G$. Suppose $\lambda_1(D)\geq \cdots \geq \lambda_n(D)$ are the $D$-eigenvalues of $G$.
Shu, Jinlong, Liu, Shuting, Xue, Jie
core   +1 more source

Novel descriptors for the prediction of molecular properties

Open Chemistry
Molecular descriptors are fundamental to the fields of cheminformatics, drug discovery, and materials science, serving as quantitative representations of molecular structures that facilitate the prediction of various properties and activities.
Nizami Abdul Rauf, Ali Sayyada Fiza, Afzal Muhammad Zia, Inc Mustafa   +3 more
doaj   +1 more source

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  

Convex and quasiconvex functions on trees and their applications

, 2017
We introduce convex and quasiconvex functions on trees and prove that for a tree the eccentricity, transmission and weight functions are strictly quasiconvex. It is shown that the Perron vector of the distance matrix is strictly convex whereas the Perron
M. Nath, Kalita, D., Sarma, D., Nath, M., R.B. Bapat, D. Kalita, Bapat, R. B., D. Sarma   +7 more
core   +1 more source

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, Díaz, Roberto C., Cardoso, Domingos M.   +2 more
core   +1 more source