Search Results (9)

Currently, Chinese villages are grappling with the issue of regional value collapse within the long-standing ‘urban-rural dual system’ strategy. Characteristic villages, as integral components of the urban–rural hierarchical spatial system and pivotal agents in rural development, wield significant influence in addressing China’s rural crises. The construction practice of characteristic villages showcases the cognitive evolution of ‘element-industry-function-type’. Within the value perception of characteristic villages, these practices reflect fundamental orientations in the interaction between humans and land, emphasizing the symbiotic relationship between production, life, and ecology. In alignment with this value perception, and drawing upon the existing studies on the classification of characteristic village types in Jixi County, this paper establishes a comprehensive type knowledge graph of characteristic villages. The framework of this graph’s expression revolves around ‘spatial elements-spatial combination-spatial organization’. This graph delineates a knowledge progression encompassing ‘information-knowledge-strategy’, characterized by three levels: the factual knowledge graph, conceptual knowledge graph and regular knowledge graph. The type knowledge graph systematically accumulates insights derived from the spatiotemporal transmission path of the village spatial structure. It formulates a structured progression of knowledge as follows: cognition of the village entity information → analysis of the village landscape structure → examination of the village social relationships. This constructed graph translates type-data information into spatial strategy knowledge, serving as a pivotal process in amalgamating characteristic village spatial data with semantic networks, particularly in expressing authenticity inspection and gene transfer. Full article

In real-world scenarios, images may be affected by additional noise during compression and transmission, which interferes with postprocessing such as image segmentation and feature extraction. Image noise can also be induced by environmental variables and imperfections in the imaging equipment. Robust principal component analysis (RPCA), one of the traditional approaches for denoising images, suffers from a failure to efficiently use the background’s low-rank prior information, which lowers its effectiveness under complex noise backgrounds. In this paper, we propose a robust PCA method based on a nonconvex low-rank approximation and total variational regularization (TV) to model the image denoising problem in order to improve the denoising performance. Firstly, we use a nonconvex $\gamma$-norm to address the issue that the traditional nuclear norm penalizes large singular values excessively. The rank approximation is more accurate than the nuclear norm thanks to the elimination of matrix elements with substantial approximation errors to reduce the sparsity error. The method’s robustness is improved by utilizing the low sensitivity of the $\gamma$-norm to outliers. Secondly, we use the $l_1$-norm to increase the sparsity of the foreground noise. The TV norm is used to improve the smoothness of the graph structure in accordance with the sparsity of the image in the gradient domain. The denoising effectiveness of the model is increased by employing the alternating direction multiplier strategy to locate the global optimal solution. It is important to note that our method does not require any labeled images, and its unsupervised denoising principle enables the generalization of the method to different scenarios for application. Our method can perform denoising experiments on images with different types of noise. Extensive experiments show that our method can fully preserve the edge structure information of the image, preserve important features of the image, and maintain excellent visual effects in terms of brightness smoothing. Full article

The transmission of a vertex v of a graph G is the sum of distances from v to all the other vertices of G. A transmission irregular graph (TI graph) has mutually distinct vertex transmissions. In 2018, Alizadeh and Klavžar posed the following question: do there exist infinite families of regular TI graphs? An infinite family of TI cubic graphs of order $118+72k$, $k\ge 0$, was constructed by Dobrynin in 2019. In this paper, we study the problem of finding TI cubic graphs for an arbitrary number of vertices. It is shown that there exists a TI cubic graph of an arbitrary even order $n\ge 22$. Almost all constructed graphs are contained in twelve infinite families. Full article

This paper discusses an evaluation method of transmission properties of networks described with regular graphs (Reference Graphs) using unevenness coefficients. The first part of the paper offers generic information about describing network topology via graphs. The terms ‘chord graph’ and ‘Reference Graph’, which is a special form of a regular graph, are defined. The operating principle of a basic tool used for testing the network’s transmission properties is discussed. The next part consists of a description of the searching procedure of the shortest paths connecting any two nodes of a graph and the method determining the number of uses of individual graph edges. The analysis shows that using particular edges of a graph depends on two factors: their total number in minimum length paths and their total number in parallel paths connecting the graph nodes. The latter makes it possible to define an unevenness coefficient. The calculated values of the unevenness coefficients can be used to evaluate the transmission properties of networks and to control the distribution of transmission resources. Full article

Given a simple connected graph G, let $D(G)$ be the distance matrix, $D^L(G)$ be the distance Laplacian matrix, $D^Q(G)$ be the distance signless Laplacian matrix, and $Tr(G)$ be the vertex transmission diagonal matrix of G. We introduce the generalized distance matrix $D_{\alpha }(G)=\alpha Tr(G)+(1-\alpha )D(G)$ , where $\alpha \in [0,1]$ . Noting that $D_0(G)=D(G),2D_{\frac{1}{2}}(G)=D^Q(G),D_1(G)=Tr(G)$ and $D_{\alpha }(G)-D_{\beta }(G)=(\alpha -\beta )D^L(G)$ , we reveal that a generalized distance matrix ideally bridges the spectral theories of the three constituent matrices. In this paper, we obtain some sharp upper and lower bounds for the generalized distance energy of a graph G involving different graph invariants. As an application of our results, we will be able to improve some of the recently given bounds in the literature for distance energy and distance signless Laplacian energy of graphs. The extremal graphs of the corresponding bounds are also characterized. Full article

Let G be a simple connected graph. In this paper, we study the spectral properties of the generalized distance matrix of graphs, the convex combination of the symmetric distance matrix $D\left(G\right)$ and diagonal matrix of the vertex transmissions $Tr\left(G\right)$ . We determine the spectrum of the join of two graphs and of the join of a regular graph with another graph, which is the union of two different regular graphs. Moreover, thanks to the symmetry of the matrices involved, we study the generalized distance spectrum of the graphs obtained by generalization of the join graph operation through their eigenvalues of adjacency matrices and some auxiliary matrices. Full article

The generalized distance matrix $D_{\alpha }\left(G\right)$ of a connected graph G is defined as $D_{\alpha }\left(G\right)=\alpha Tr\left(G\right)+(1-\alpha )D\left(G\right)$ , where $0\le \alpha \le 1$ , $D\left(G\right)$ is the distance matrix and $Tr\left(G\right)$ is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy $E^{D_{\alpha }}\left(G\right)$ . Some new upper and lower bounds for the generalized distance energy $E^{D_{\alpha }}\left(G\right)$ of G are established based on parameters including the Wiener index $W\left(G\right)$ and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n. Full article

Let G be a simple undirected graph containing n vertices. Assume G is connected. Let $D(G)$ be the distance matrix, $D^L(G)$ be the distance Laplacian, $D^Q(G)$ be the distance signless Laplacian, and $Tr(G)$ be the diagonal matrix of the vertex transmissions, respectively. Furthermore, we denote by $D_{\alpha }(G)$ the generalized distance matrix, i.e., $D_{\alpha }(G)=\alpha Tr(G)+(1-\alpha )D(G)$ , where $\alpha \in [0,1]$ . In this paper, we establish some new sharp bounds for the generalized distance spectral radius of G, making use of some graph parameters like the order n, the diameter, the minimum degree, the second minimum degree, the transmission degree, the second transmission degree and the parameter $\alpha$ , improving some bounds recently given in the literature. We also characterize the extremal graphs attaining these bounds. As an special cases of our results, we will be able to cover some of the bounds recently given in the literature for the case of distance matrix and distance signless Laplacian matrix. We also obtain new bounds for the k-th generalized distance eigenvalue. Full article

For a simple undirected connected graph G of order n, let $D\left(G\right)$ , $D^L\left(G\right)$ , $D^Q\left(G\right)$ and $Tr\left(G\right)$ be, respectively, the distance matrix, the distance Laplacian matrix, the distance signless Laplacian matrix and the diagonal matrix of the vertex transmissions of G. The generalized distance matrix $D_{\alpha }\left(G\right)$ is signified by $D_{\alpha }\left(G\right)=\alpha Tr\left(G\right)+(1-\alpha )D\left(G\right)$ , where $\alpha \in [0,1].$ Here, we propose a new kind of Estrada index based on the Gaussianization of the generalized distance matrix of a graph. Let ${\partial }_1,{\partial }_2,\dots ,{\partial }_n$ be the generalized distance eigenvalues of a graph G. We define the generalized distance Gaussian Estrada index $P_{\alpha }\left(G\right)$ , as $P_{\alpha }\left(G\right)={\sum }_{i=1}^n{e}^{-{\partial }_i^2}.$ Since characterization of $P_{\alpha }\left(G\right)$ is very appealing in quantum information theory, it is interesting to study the quantity $P_{\alpha }\left(G\right)$ and explore some properties like the bounds, the dependence on the graph topology G and the dependence on the parameter $\alpha$ . In this paper, we establish some bounds for the generalized distance Gaussian Estrada index $P_{\alpha }\left(G\right)$ of a connected graph G, involving the different graph parameters, including the order n, the Wiener index $W\left(G\right)$ , the transmission degrees and the parameter $\alpha \in [0,1]$ , and characterize the extremal graphs attaining these bounds. Full article