Bounds for the Generalized Distance Eigenvalues of a Graph [PDF]
, 2019 Let G be a simple undirected graph containing n vertices. Assume G is connected. Let D(G) be the distance matrix, DL(G) be the distance Laplacian, DQ(G) be the distance signless Laplacian, and Tr(G) be the diagonal matrix of the vertex transmissions ...
Abdollah Alhevaz +7 more
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Distance signless Laplacian eigenvalues, diameter, and clique number [PDF]
Discrete Mathematics Letters, 2022 Saleem Khan, Shariefuddin Pirzada
doaj +1 more source
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 +7 more
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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
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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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On energy of prime ideal graph of a commutative ring associated with transmission-based matrices [PDF]
This research explores the energy of the prime ideal graph of a commutative ring. The study demonstrates the energy formula of the graph associated with transmission-based matrices.
Purnamasari, N.A. +4 more
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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
On the distance signless Laplacian spectral radius, fractional matching and factors of graphs
The distance signless Laplacian matrix of a graph $G$ is define as $Q(G)=$Tr$(G)+D(G)$, where Tr$(G)$ and $D(G)$ are the diagonal matrix of vertex transmissions and the distance matrix of $G$, respectively. Denote by $E_G(v)$ the set of all edges incident to a vertex $v$ in $G$.
Zhang, Z. H., Wang, L. G.
openaire +2 more sources
On the sum of powers of Laplacian eigenvalues of bipartite graphs [PDF]
, 2010 summary:For a bipartite graph $G$ and a non-zero real $\alpha $, we give bounds for the sum of the $\alpha $th powers of the Laplacian eigenvalues of $G$ using the sum of the squares of degrees, from which lower and upper bounds for the incidence ...
Ilić, Aleksandar, Zhou, Bo
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Distance spectral conditions for $ID$-factor-critical and fractional $[a, b]$-factor of graphs
, 2023 Let $G=(V(G), E(G))$ be a graph with vertex set $V(G)$ and edge set $E(G)$. A graph is $ID$-factor-critical if for every independent set $I$ of $G$ whose size has the same parity as $|V(G)|$, $G-I$ has a perfect matching.
Wang, Ligong, Ma, Tingyan
core