相关论文: Beyond graph energy: norms of graphs and matrices

In this paper, we determine the Randic' energy of the m-splitting graph, the m-shadow graph and the m-duplicate graph of a given graph, m being an arbitrary integer. Our results allow the construction of an infinite sequence of graphs…

The area of Data Analytics on graphs promises a paradigm shift as we approach information processing of classes of data, which are typically acquired on irregular but structured domains (social networks, various ad-hoc sensor networks).…

For a Hermitian matrix $A$ of order $n$ with eigenvalues $\lambda_1(A)\ge \cdots\ge \lambda_n(A)$, define \[ \mathcal{E}_p^+(A)=\sum_{\lambda_i > 0} \lambda_i^p(A), \quad \mathcal{E}_p^-(A)=\sum_{\lambda_i<0} |\lambda_i(A)|^p,\] to be the…

The eccentricity matrix $\epsilon(G)$, of a connected graph $G$ is obtained by retaining the maximum distance from each row and column of the distance matrix of $G$ and the other entries are assigned with 0. In this paper, we discuss the…

Recent years have witnessed the promise that reinforcement learning, coupled with Graph Neural Network (GNN) architectures, could learn to solve hard combinatorial optimization problems: given raw input data and an evaluator to guide the…

We present a diagrammatic approach to construct self-energy approximations within many-body perturbation theory with positive spectral properties. The method cures the problem of negative spectral functions which arises from a…

Lattices are architected metamaterials whose properties strongly depend on their geometrical design. The analogy between lattices and graphs enables the use of graph neural networks (GNNs) as a faster surrogate model compared to traditional…

We study entanglement properties of mixed density matrices obtained from combinatorial Laplacians. This is done by introducing the notion of the density matrix of a graph. We characterize the graphs with pure density matrices and show that…

In this paper, we define and obtain several properties of the (adjacency) energy of a hypergraph. In particular, bounds for this energy are obtained as functions of structural and spectral parameters, such as Zagreb index and spectral…

We investigate the spatial statistics of the energy eigenfunctions on large quantum graphs. It has previously been conjectured that these should be described by a Gaussian Random Wave Model, by analogy with quantum chaotic systems, for…

Let $G$ be a simple graph with vertex set $V(G) = \{v_1, v_2,\ldots, v_n\}$. The Sombor matrix of $G$, denoted by $A_{SO}(G)$, is defined as the $n\times n$ matrix whose $(i,j)$-entry is $\sqrt{d_i^2+d_j^2}$ if $v_i$ and $v_j$ are adjacent…

For a simple graph $G$ with $n$ vertices, let $A_G$ denote the adjacency matrix of $G$, and let $\lambda_1(G) \geq \lambda_2(G) \geq \dots \geq \lambda_n(G)$ be its eigenvalues. For an integer $p \geq 2$, the positive $p$-energy and…

Many natural and social systems develop complex networks, that are usually modelled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semi-circle law is known to…

A vertex-degree-based topological index named as Sombor index of a simple graph G with n vertices was recently introduced by I. Gutman. In this paper, we find Sombor index of m-splitting graph and m-shadow graph. Also, we determine relation…

The energy of a graph is defined as the sum of the absolute values of the eigenvalues of the graph. In this paper, we present a new method to compare the energies of two $k$-subdivision bipartite graphs on some cut edges. As the…

Finding a new mathematical representations for graph, which allows direct comparison between different graph structures, is an open-ended research direction. Having such a representation is the first prerequisite for a variety of machine…

The energy of a simple graph $G$ arising in chemical physics, denoted by $\mathcal E(G)$, is defined as the sum of the absolute values of eigenvalues of $G$. We consider the asymptotic energy per vertex (say asymptotic energy) for lattice…

The eccentricity matrix of a graph is obtained from the distance matrix by keeping the largest entries in their row or column, and the remaining entries are replaced by zeros. The eccentricity energy of a graph is the sum of the absolute…

Let $\Gamma$ be a connected regular graph with an eigenvalue $\lambda$ and corresponding idempotent $E_{\lambda}$. Let ${\cal E}_{\lambda}=\langle J,E_{\lambda}\rangle^\circ$ be the algebra generated by $J$ and $E_\lambda$ with respect to…

We consider circulant graphs G(r,N) where the vertices are the integers modulo N and the neighbours of 0 are {-r,...,-1,1,...,r}. The energy of G(r,N) is a trigonometric sum of N*r terms. For low values of r we compute this sum explicitly.…