Eigenvalues Of Adjacency Matrix Research Articles

Some stable and closed-shell structures of anticancer drugs by graph theoretical parameters

The eigenvalues are significant in mathematics, but they are also relevant in other domains like as chemistry, economics, and a variety of others. In terms of our research, eigenvalues are used in chemistry to represent not only the form of energy but also the various physicochemical aspects of a chemical substance. We must comprehend the connection between mathematics and chemistry. The antibonding level is related to positive eigenvalues, the bonding level is associated to negative eigenvalues, and the nonbonding level is linked to zero eigenvalues. In this work, we studied some anticancer drug structures in terms of nullity, matching number, eigenvalues of adjacency matrix, and characteristics polynomials. As a result, Carmustine, Caulibugulone-E, Aspidostomide-E anticancer drug structures are stable, closed-shell molecules since their nullity is equal to zero.

The Maximum Eigenvalue of the Brain Functional Network Adjacency Matrix: Meaning and Application in Mental Fatigue Evaluation.

The maximum eigenvalue of the adjacency matrix (AM) has been supposed to contain rich information about the corresponding network. An experimental study focused on revealing the meaning and application of the maximum eigenvalue is missing. To this end, AM was constructed using mutual information (MI) to determine the functional connectivity with electroencephalogram (EEG) data recorded with a mental fatigue model, and then was converted into both binary and weighted brain functional network (BFN) and corresponding random networks (RNs). Both maximum eigenvalue and corresponding network characters in BFNs and RNs were considered to explore the changes during the formation of mental fatigue. The results indicated that large maximum eigenvalue means more edges in the corresponding network, along with a high degree and a short characteristic path length both in weighted and binary BFNs. Interestingly, the maximum eigenvalue of AM was always a little larger than that of the corresponding random matrix (RM), and had an obvious linearity with the sum of the AM elements, indicating that the maximum eigenvalue can be able to distinguish the network structures which have the same mean degree. What is more, the maximum eigenvalue, which increased with the deepening of mental fatigue, can become a good indicator for mental fatigue estimation.

On the spectrum of linear dependence graph of a finite dimensional vector space

In this article, we introduce and characterize linear dependence graph Γ( V ) of a finite dimensional vector space V over a finite field of q elements. Two vector spaces U and V are isomorphic if and only if their linear dependence graphs Γ( U ) and Γ( V ) are isomorphic. The linear dependence graph Γ( V ) is Eulerian if and only if q is odd. Highly symmetric nature of Γ( V ) is reflected in its automorphism group S m ⊕ ( ⊕ i = 1 m S q − 1 ) , where m = ( q n − 1)/( q − 1) . Besides these basic characterizations of Γ( V ) , the main contribution of this article is to find eigen values of adjacency matrix, Laplacian matrix and distance matrix of this graph.

Eigenvalues and diameter

Let G be a connected graph of order n. The diameter of a graph is the maximum distance between any two vertices of G. In this paper, we will give some bounds on the diameter of G in terms of eigenvalues of adjacency matrix and Laplacian matrix, respectively.

Phased graphs and graph energies

We define a phased graph G to yield an adjacency matrix A(G) having general magnitude-1 values in the same locations as the usual unphased case, but subject to the restriction that A be Hermitian. Some characteristics of such phased graphs and their eigenspectra are contemplated and to some extent described. Different graph energies are defined as suitable sums over adjacency-matrix eigenvalues, with “occupation-number” coefficients \({\in \{0,1, 2\}}\).

Toxicity Mode‐of‐action: Discrimination via Infrared Spectra And Eigenvalues of the Modified Adjacency Matrix

AbstractAquatic toxicity can be partitioned into a number of mechanisms of action, the allocation of a given chemical to its particular mode being of fundamental importance for the toxicological risk assessment. We investigated the possibility to automatically allocate each chemical to its putative aquatic toxicity mode‐of‐action on the basis of the sole chemical physical information. In this paper, we refer to the four mode‐of‐action classes defined in Hermens' laboratory [1, 2]; the chemical descriptors used were the Infrared spectra and the Burden's Modified Adjacency Matrix Eigenvalues. At odds with Infrared spectrum, the Eigenvalues were able to allocate the chemicals into the different mechanism of action classes via a nonlinear discrimination method (K‐nearest neighbours classifier).