cospectrality of two graphs measures the differences between the ordered spectrum of these graphs in various ways. actually,the origin of this concept came back to richard brualdi's problems that are proposed in cite{braldi}:let $g_n$ and $g'_n$ be two nonisomorphic simple graphs on $n$ vertices with spectra$$lambda_1 geq lambda_2 geq cdots geq lambda_n ;;;text{and};;; lambda'_1 geq lambda'_2 g...

Spectral graph theory discusses about the algebraic properties of graphs based on spectrum a graph. This article investigated prism The method used in this research is circulant matrix. results showed that P2,s regular degree 3, for s odd and ≥ circulantt with spectrum.

Graph convolutional network (GCN) architecture is the basis of many neural networks and has been widely used in processing graph-structured data. When dealing with large sparse data, deeper GCN models are often required. However, suffer from performance degradation as number layers increases. The mainstream attribution current research over-smoothing, there also gradient vanishing, training dif...

The spectrum of a graph has been widely used in graph theory to characterise the properties of a graph and extract information from its structure. It has been less popular as a representation for pattern matching for two reasons. Firstly, more than one graph may share the same spectrum. It is well known, for example, that very few trees can be uniquely specified by their spectrum. Secondly, the...

in the process of structural analysis we often come to structures that can be analyzed with simpler methods than the standard approaches. for these structures, known as regular structures, the matrices involved are in canonical forms and their eigen-solution can be performed in a simple manner. however, by adding or removing some elements or nodes, such methods cannot be utilized. here, an effi...

The spectrum of a graph has been widely used in graph theory to characterise the properties of a graph and extract information from its structure. It has also been employed as a graph representation for pattern matching since it is invariant to the labelling of the graph. There are however a number of potential drawbacks in using the spectrum as a representation of a graph; Firstly, more than o...

If G is an (n,m)-graph whose spectrum consists of the numbers λ1, λ2, . . . , λn, then its Estrada index is EE(G) = ∑n i=1 e λi . We establish lower bounds for EE(G) in terms of n and m. Introduction In this paper we are concerned with simple graphs, that have no loops and no multiple or directed edges. Let G be such a graph, and let n and m be the number of its vertices and edges. Then we say ...

The spectrum of a network or graph G = (V,E) with adjacency matrix A, consists of the eigenvalues of the normalized Laplacian L = I − D−1/2AD−1/2. This set of eigenvalues encapsulates many aspects of the structure of the graph, including the extent to which the graph posses community structures at multiple scales. We study the problem of approximating the spectrum λ = (λ1, . . . , λ|V |), 0 ≤ λ...