Results 1 to 10 of about 211,399 (214)
On the Wiener index, distance cospectrality and transmission-regular graphs [PDF]
Discrete Applied Mathematics, 2017 In this paper, we investigate various algebraic and graph theoretic properties of the distance matrix of a graph. Two graphs are $D$-cospectral if their distance matrices have the same spectrum. We construct infinite pairs of $D$-cospectral graphs with different diameter and different Wiener index.
Aida Abiad +7 more
+7 more sources
On the Largest Distance (Signless Laplacian) Eigenvalue of Non-transmission-regular Graphs
The Electronic Journal of Linear Algebra, 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 $G$. The transmission of $v_i \in V(G)$, denoted by $Tr_G(v_i)$ is defined to be the sum of distances from $v_i$ to all other vertices of $G$, i.e., the ...
Liu, Shuting, Shu, Jinlong, Xue, Jie
openaire +3 more sources
On the $D_α$ spectral radius of non-transmission regular graphs [PDF]
Let $G$ be a connected graph with order $n$ and size $m$. Let $D(G)$ and $Tr(G)$ be the distance matrix and diagonal matrix with vertex transmissions of $G$, respectively. For any real $α\in[0,1]$, the generalized distance matrix $D_α(G)$ of $G$ is defined as $$D_α(G)=αTr(G)+(1-α)D(G).$$ The largest eigenvalue of $D_α(G)$ is called the $D_α$ spectral ...
Xu, Zengzhao, Xi, Weige, Wang, Ligong
openaire +3 more sources
A characterization of extremal non-transmission-regular graphs by the distance (signless Laplacian) spectral radius [PDF]
Let $G$ be a simple connected graph of order $n$ and $\partial(G)$ is the spectral radius of the distance matrix $D(G)$ of $G$. The transmission $D_i$ of vertex $i$ is the $i$-th row sum of $D(G)$. Denote by $D_{\max}(G)$ the maximum of transmissions over all vertices of $G$, and $\partial^Q(G)$ is the spectral radius of the distance signless Laplacian
Lan, Jingfen, Liu, Lele
openaire +3 more sources
On comparison between the distance energies of a connected graph [PDF]
HeliyonLet G be a simple connected graph of order n having Wiener index W(G). The distance, distance Laplacian and the distance signless Laplacian energies of G are respectively defined asDE(G)=∑i=1n|υiD|,DLE(G)=∑i=1n|υiL−Tr‾|andDSLE(G)=∑i=1n|υiQ−Tr‾|, where ...
Hilal A. Ganie +2 more
doaj +2 more sources
NEW BOUNDS AND EXTREMAL GRAPHS FOR DISTANCE SIGNLESS LAPLACIAN SPECTRAL RADIUS [PDF]
Journal of Algebraic Systems, 2021 The distance signless Laplacian spectral radius of a connected graph $G$ is the largest eigenvalue of the distance signless Laplacian matrix of $G$, defined as $D^{Q}(G)=Tr(G)+D(G)$, where $D(G)$ is the distance matrix of $G$ and $Tr(G)$ is the diagonal ...
A. Alhevaz, M. Baghipur, S. Paul
doaj +1 more source
Some inequalities involving the distance signless Laplacian eigenvalues of graphs [PDF]
Transactions on Combinatorics, 2021 Given a simple graph $G$, the distance signlesss Laplacian $D^{Q}(G)=Tr(G)+D(G)$ is the sum of vertex transmissions matrix $Tr(G)$ and distance matrix $D(G)$.
Abdollah Alhevaz +3 more
doaj +1 more source
On Transmission Irregular Cubic Graphs of an Arbitrary Order
Mathematics, 2022 The transmission of a vertex v of a graph G is the sum of distances from v to all the other vertices of G. A transmission irregular graph (TI graph) has mutually distinct vertex transmissions.
Anatoly Yu. Bezhaev, Andrey A. Dobrynin
doaj +1 more source
Land, 2023 Currently, Chinese villages are grappling with the issue of regional value collapse within the long-standing ‘urban-rural dual system’ strategy. Characteristic villages, as integral components of the urban–rural hierarchical spatial system and pivotal ...
Kai Ren, Khaliun Buyandelger
doaj +1 more source
Large-scale power inspection: A deep reinforcement learning approach
Frontiers in Energy Research, 2023 Power inspection plays an important role in ensuring the normal operation of the power grid. However, inspection of transmission lines in an unoccupied area is time-consuming and labor-intensive.
Qingshu Guan +6 more
doaj +1 more source