Results 21 to 30 of about 13,640 (282)
On Eccentricity Version of Laplacian Energy of a Graph [PDF]
Mathematics Interdisciplinary Research, 2017 The energy of a graph G is equal to the sum of absolute values of the eigenvalues of the adjacency matrix of G, whereas the Laplacian energy of a graph G is equal to the sum of the absolute value of the difference between the eigenvalues of the Laplacian
Nilanjan De
doaj +1 more source
Kernels of Directed Graph Laplacians [PDF]
The Electronic Journal of Combinatorics, 2006 Let $G$ denote a directed graph with adjacency matrix $Q$ and in-degree matrix $D$. We consider the Kirchhoff matrix $L=D-Q$, sometimes referred to as the directed Laplacian. A classical result of Kirchhoff asserts that when $G$ is undirected, the multiplicity of the eigenvalue 0 equals the number of connected components of $G$.
Caughman, John S., IV, Veerman, J. J. P.
openaire +2 more sources
Discrete Mathematics, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kinkar Chandra Das, Seyed Ahmad Mojallal
openaire +1 more source
Hermitian Laplacian Matrix of Directed Graphs [PDF]
Jisuanji kexue, 2023 Laplacian matrix plays an important role in the research of undirected graphs.From its spectrum,some structure and properties of a graph can be deduced.Based on this,several efficient algorithms have been designed for relevant tasks in graphs,such as ...
LIU Kaiwen, HUANG Zengfeng
doaj +1 more source
On the Laplacian spread of graphs
Applied Mathematics Letters, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mingqing Zhai +2 more
openaire +2 more sources
On net-Laplacian energy of signed graphs
Communications in Combinatorics and Optimization, 2017 A signed graph is a graph where the edges are assigned either positive or negative signs. Net degree of a signed graph is the difference between the number of positive and negative edges incident with a vertex. It is said to be net-regular if all its
Nutan G. Nayak
doaj +1 more source
International Journal of Robust and Nonlinear Control, EarlyView., 2023 Abstract We propose a hierarchical energy management scheme for aggregating Distributed Energy Resources (DERs) for grid flexibility services. To prevent a direct participation of numerous prosumers in the wholesale electricity market, aggregators, as self‐interest agents in our scheme, incentivize prosumers to provide flexibility. We firstly model the
Xiupeng Chen +3 more
wiley +1 more source
The fan graph is determined by its signless Laplacian spectrum [PDF]
, 2020 summary:Given a graph $G$, if there is no nonisomorphic graph $H$ such that $G$ and $H$ have the same signless Laplacian spectra, then we say that $G$ is \hbox {$Q$-DS}.
Yuan, Yuan +2 more
core +1 more source
A novel method to construct cospectral graphs based on RT operation [PDF]
AIP AdvancesThis paper presents a new graph operation, RT(G), which is formed by transforming each vertex and edge of the original graph G into a triangle. We analyze the relationship between the signless Laplacian characteristic polynomials of the graph RT(G) and ...
Xiu-Jian Wang +2 more
doaj +1 more source
Tarantula graphs are determined by their Laplacian spectrum
Electronic Journal of Graph Theory and Applications, 2021 A graph G is said to be determined by its Laplacian spectrum (DLS) if every graph with the same Laplacian spectrum is isomorphic to G. A graph which is a collection of hexagons (lengths of these cycles can be different) all sharing precisely one vertex ...
Reza Sharafdini, Ali Zeydi Abdian
doaj +1 more source