Results 1 to 10 of about 252,641 (311)

The energy of graphs and matrices

Journal of Mathematical Analysis and Applications, 2007
We extend the concept of graph energy, introduced by Gutman, to matrices. We give upper and lower bounds on matrix energy extending previous results for graphs. In particular, we estimate the energy of almost all graphs.
openaire   +2 more sources

On the locating matrix of a graph and its spectral analysis [PDF]

Computer Science Journal of Moldova, 2017
We introduce a new matrix representation for a graph by defining the locating matrix $\mathbf{Lo}(G)$ of $G$. We define the locating eigenvalues, the locating spectrum, and locating energy of the graph and we calculate them for some standard graphs.
H. N. Ramaswamy, Anwar Alwardi, N. Ravi Kumar   +2 more
doaj  

Vertex weighted Laplacian Energy of union of graphs [PDF]

Computer Science Journal of Moldova, 2018
The vertex weighted Laplacian energy with respect to the vertex weight $w$ of a graph $G$ with $n$ vertices is defined as ~$LE_w(G)=\sum\limits_{i=1}^n|\mu_i-\bar{w}|$, where ${{\mu }_{1}},{{\mu }_{2}},...,{{\mu }_{n}}$ are the Laplacian eigenvalues of ...
Nilanjan De
doaj  

-borderenergetic graphs

AKCE International Journal of Graphs and Combinatorics, 2020
A graph is said to be borderenergetic (-borderenergetic, respectively) if its energy (Laplacian energy, respectively) equals the energy (Laplacian energy, respectively) of the complete graph .
Qingyun Tao, Yaoping Hou
doaj   +1 more source

Control Energy of Lattice Graphs [PDF]

2018 IEEE Conference on Decision and Control (CDC), 2018
7 pages, 3 figures, for CDC ...
Isaac S. Klickstein, Francesco Sorrentino 0001   +1 more
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Energy Conditions for Hamiltonian and Traceable Graphs

Universal Journal of Mathematics and Applications, 2019
A graph is called Hamiltonian (resp. traceable) if the graph has a Hamiltonian cycle (resp. path), a cycle (resp. path) containing all the vertices of the graph. The energy of a graph is defined as the sum of the absolute values of the eigenvalues of the
Rao Li
doaj   +1 more source

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

Computing the dependence of graph energy on nullity: The method of siblings [PDF]

Discrete Mathematics Letters, 2021
Ivan Gutman
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Seidel Laplacian Energy of Fuzzy graphs

EAI Endorsed Transactions on Energy Web
The energy of a graph is related to its spectrum, which is equal to the total of the latent values of the pertinent adjacency matrix. In this research work, we proposed some of the features and the energy of the Seidel Laplacian of a fuzzy graph.
K Sivaranjani, O V Shanmuga Sundaram, K Akalyadevi   +2 more
doaj   +1 more source

Note on the Randic energy of graphs [PDF]

Kragujevac Journal of Mathematics, 2018
Summary: If \(G\) is a graph on \(n\) vertices, and \(d_i\) is the degree of its \(i\)-th vertex, then the Randic matrix of \(G\) is the square matrix of order \(n\) whose \((i, j)\)-entry is equal to \(1/\sqrt{d_id_j}\) if the \(i\)-th and \(j\)-th vertex of \(G\) are adjacent, and zero otherwise.
He, Jun, Liu, Yan-Min, Tian, Jun-Kang
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