Search Results (162)

An interconnection network is usually modeled by a graph, and fault tolerance of the interconnection network is often measured by connectivity of the graph. Given a connected subgraph L of a graph G and non-negative integer t, the t-extra connectivity ${\kappa }_t\left(G\right)$, the L-structure connectivity $\kappa (G;L)$ and the t-extra L-structure connectivity ${\kappa }_g(G;L)$ of G can provide new metrics to measure the fault tolerance of a network represented by G. Fully connected cubic networks ${\mathcal{FC}}_n$ are a class of hierarchical networks which enjoy the strengths of a constant vertex degree and good expansibility. In this paper, we determine ${\kappa }_t\left({\mathcal{FC}}_n\right)$, $\kappa ({\mathcal{FC}}_n;L)$ and ${\kappa }_t({\mathcal{FC}}_n;L)$ for $t=1$ and $L\in \{K_{1,1},K_{1,2},K_{1,3}\}$. We also establish the edge versions ${\lambda }_t\left({\mathcal{FC}}_n\right)$, $\lambda ({\mathcal{FC}}_n;L)$ and ${\lambda }_t({\mathcal{FC}}_n;L)$ for $t=1$ and $L\in \{K_{1,1},K_{1,2}\}$. Full article

Kidney-paired donation programs assist patients in need of a kidney to swap their incompatible donor with another incompatible patient–donor pair for a suitable kidney in return. The kidney exchange problem (KEP) is a mathematical optimization problem that consists of finding the maximum set of matches in a directed graph representing the pool of incompatible pairs. Depending on the specific framework, these matches can come in the form of (bounded) directed cycles or directed paths. This gives rise to a family of KEP models that have been studied over the past few years. Several of these models require an exponential number of constraints to eliminate cycles and chains that exceed a given length. In this paper, we present enhancements to a subset of existing models that exploit the connectivity properties of the underlying graphs, thereby rendering more compact and tractable models in both cycle-only and cycle-and-chain versions. In addition, an efficient algorithm is developed for detecting violated constraints and solving the problem. To assess the value of our enhanced models and algorithm, an extensive computational study was carried out comparing with existing formulations. The results demonstrated the effectiveness of the proposed approach. For example, among the main findings for edge-based cycle-only models, the proposed (*PRE(i)) model uses a new set of constraints and a small subset of the full set of length-k paths that are included in the edge formulation. The proposed model was observed to achieve a more than 98% reduction in the number of such paths among all tested instances. With respect to cycle-and-chain formulations, the proposed (*ReSPLIT) model outperformed Anderson’s arc-based (AA) formulation and the path constrained-TSP formulation on all instances that we tested. In particular, when tested on a difficult sets of instances from the literature, the proposed (*ReSPLIT) model provided the best results compared to the AA and PC-based models. Full article

Extended connectivity in graphs can be analyzed through k-path Laplacian matrices, which permit the capture of long-range interactions in various real-world networked systems such as social, transportation, and multi-agent networks. In this work, we present several alternative methods based on machine learning methods (LSTM, xLSTM, Transformer, XGBoost, and ConvLSTM) to predict the final consensus value based on directed networks (Erdös–Renyi, Watts–Strogatz, and Barabási–Albert) and on the initial state. We highlight how different k-hop interactions affect the performance of the tested methods. This framework opens new avenues for analyzing multi-scale diffusion processes in large-scale, complex networks. Full article

New assembly methods for aircraft structural parts, such as skins and stringers, are being investigated to address issues like galvanic corrosion, stress concentration, and weight. For this, many researchers are examining the mechanical and fracture properties of adhesively bonded parts through experimental testing and numerical modelling methods, including Cohesive Zone Modelling (CZM), Compliance-Based Beam Method (CBBM), Double Cantilever Beam (DCB), and End Notched Flexural (ENF) tests. In this study, similarly, DCB and ENF tests were conducted on skin and beam parts bonded with AF163-2K adhesive using CBBM and then modelled and analysed in ABAQUS CAE 2018 software. Four different skin–stringer connection models were analysed, respectively, using only adhesive, only rivets, both adhesive and rivets, and also a reduced number of rivets in the adhesively bonded joint. This study found that adhesive increased initial strength, while rivets improved strength after the adhesive began to crack. Using a hybrid connection that combines both rivets and adhesive has been observed to enhance the overall strength and durability of the assembly. Then, experimental results were compared, and four numerical models for skin–stringer connections (adhesive only, rivets only, adhesive and rivets, and adhesive with reduced rivets) were analysed and discussed. In this context, the results were supported and reported with graphs, tables, and analysis images. Full article

In this paper, we present a graph-based analysis of the topology of D-Wave quantum computers, focusing on the Pegasus, Chimera, and Zephyr architectures. We investigate these topologies under different parameter settings using k-hop-based graph metrics. Each of these architectures comprises distinct subgraphs in which qubits are interconnected according to specific patterns dictated by their implementation. Our study pursues two primary objectives. First, we analyze the structural properties of the Chimera, Pegasus, and Zephyr topologies, examining their scalability and connectivity characteristics. Second, we evaluate the behavior of graph-based density and redundancy metrics within these architectures. The inherent symmetries of these quantum hardware designs provide a unique opportunity to systematically assess the effectiveness of these metrics across varying connectivity patterns. By leveraging these symmetries, our findings not only enhance the understanding of these topological structures but also offer deeper insights into the reliability and applicability of the proposed metrics in the broader context of quantum hardware design. Full article

With the rapid development of remote sensing technology, the question of how to leverage large amounts of unlabeled remote sensing data to detect changes in multi-temporal images has become a significant challenge. Self-supervised methods (SSL) for remote sensing image change detection (CD) can effectively address the issue of limited labeled data. However, most SSL algorithms for CD in remote sensing image rely on convolutional neural networks with fixed receptive fields as their feature extraction backbones, which limits their ability to capture objects of varying scales and model global contextual information in complex scenes. Additionally, these methods fail to capture essential topological and structural information from remote sensing images, resulting in a high false positive rate. To address these issues, we introduce a graph diffusion model into the field of CD and propose a novel network architecture called CGD-CD Net, which is driven by a structure-sensitive SSL strategy based on contrastive learning. Specifically, a superpixel segmentation algorithm is applied to bi-temporal images to construct graph nodes, while the k-nearest neighbors algorithm is used to define edge connections. Subsequently, a diffusion model is employed to balance the states of nodes within the graph, enabling the co-evolution of adjacency relationships and feature information, thereby aggregating higher-order feature information to obtain superior feature embeddings. The network is trained with a carefully crafted contrastive loss function to effectively capture high-level structural information. Ultimately, high-quality difference images are generated from the extracted bi-temporal features, then use thresholding analysis to obtain a final change map. The effectiveness and feasibility of the suggested method are confirmed by experimental results on three different datasets, which show that it performs better than several of the top SSL-CD methods. Full article

It has been conjectured that for each positive integer k and each tree T with bipartite $(Z_1,Z_2)$, every k-connected bipartite graph G with $\delta \left(G\right)\ge k+max\left\{\right|Z_1|,|Z_2\left|\right\}$ admits a subgraph $T^{\prime }\cong T$ such that $G-V\left(T^{\prime }\right)$ is still k-connected. In this paper, we generalize the ear decompositions of 2-connected graphs into a $(k,a_k)$-extensible system for a general k-connected graph. As a result, we confirm the conjecture for $k\le 3$ by proving a slightly stronger version of it. Full article

The use of the Visibility Graph Algorithm (VGA) has proven to be a valuable tool for analyzing both real and synthetic seismicity series. Specifically, VGA transforms time series into a network representation in which structural properties such as node connectivity, clustering, and community structure can be quantitatively measured, thereby revealing underlying correlations and dynamics that may remain hidden in traditional linear or spectral analyses. The time series transformation into complex networks with VGA provides a new approach to analyze seismic dynamics, allowing scientists to extract trends and behaviors that may not be possible by classical time-series analysis. On the other hand, many studies attempt to find viable trends in order to identify preparation mechanisms prior to a strong earthquake or to analyze the aftershocks. In this work, the seismic activity of Southern California Earthquake was analyzed focusing only on the significant earthquakes. For this purpose, seismic series preceding and following each earthquake were constructed using a windowing method with different overlaps and the slope of the connectivity (k) versus magnitude (M) graph (k-M slope) and the average degree were computed from the mapped complex networks. The results revealed a significant decrease in these parameters after the earthquake, due to the contribution of the aftershocks from the main event. Interestingly, the study was extended to synthetic seismicity series and the same behavior was observed for both k-M slope and average degree. This finding suggests that the spring-block model reproduces a relaxation mechanism following a large-magnitude event like those of real seismic aftershocks. However, this conclusion contrasts with conclusions drawn by other researchers. These results highlight the utility of VGA in studying events that precede and follow major earthquakes. This technique may be used to extract some useful trends in seismicity, which could eventually be employed for a deeper understanding and possible forecasting of seismic behavior. Full article

Broadcasting is a fundamental information dissemination problem in a connected network where one node, referred to as the originator, must distribute a message to all other nodes through a series of calls along the network’s links. Once informed, nodes assist the originator by forwarding the message to their neighbors. Determining the broadcast time for a node in an arbitrary network is NP-complete. While polynomial-time algorithms exist for specific network topologies, the problem remains open for many others. In this paper, we focus on addressing the broadcasting problem in network topologies represented by specialized clique-based structures. Specifically, we investigate the windmill graph $W{d}_{k,l}$, which consists of k cliques of size l connected to a universal node, and extend our study to the star of cliques, a generalization of the windmill graph with cliques of arbitrary sizes. Our primary objective is to propose an efficient algorithm for determining the broadcast time of any node in an arbitrary star of cliques and to rigorously prove its optimality. Additionally, we broaden the scope by examining the broadcasting problem in path-connected cliques, a topology featuring k cliques of varying sizes sequentially connected along a path. For this structure, we develop a computationally efficient algorithm that leverages clique sizes and adjacency to optimize broadcast strategies, with broader implications for understanding communication in block graphs. Full article

Aircraft sensors are crucial for ensuring the safe and efficient operation of aircraft. However, these sensors are vulnerable to external factors that can lead to malfunctions, making fault diagnosis essential. Traditional deep learning-based fault diagnosis methods often face challenges, such as limited data representation and insufficient feature extraction. To address these problems, this paper proposes an enhanced GraphSage-based fault diagnosis method that incorporates attention mechanisms. First, signal data representing the coupling characteristics of various sensors are constructed through data stacking. These signals are then transformed into graph data with a specific topology reflecting the overall sensor status of the aircraft using K-nearest neighbor and Radius classification algorithms. This approach helps fully leverage the correlations between data points. Next, node and neighbor information is aggregated through graph sampling and attention-based aggregation methods, strengthening the extraction of fault features. Finally, fault diagnosis is performed using multi-layer aggregation and transformation within fully connected layers. Experiments demonstrate that the proposed method outperforms baseline approaches, achieving better detection performance and faster computational speed. The method has been validated on both simulated and real-flight data. Full article

Several topological indices are possibly the most widely applied graph-based molecular structure descriptors in chemistry and pharmacology. The capacity of topological indices to discriminate is a crucial component of their study. In light of this, the literature has introduced the exponential vertex-degree-based topological index. The exponential atom-bond connectivity index is defined as follows: $e^{\mathcal{ABC}}=e^{\mathcal{ABC}}({\rm Y})={\displaystyle \sum _{v_i{v}_j\in E({\rm Y})}}{e}^{\sqrt{{\displaystyle \frac{d_i+d_j-2}{d_i{d}_j}}}},$ where $d_i$ is the degree of the vertex $v_i$ in ${\rm Y}$. In this paper, we prove that the double star $D{S}_{n-3,1}$ is the second maximal graph with respect to the $e^{\mathcal{ABC}}$ index of trees of order n. We give an upper bound on $e^{\mathcal{ABC}}$ of unicyclic graphs of order n and characterize the maximal graphs. The graph $K_1\vee (P_3\cup (n-4)K_1)$ gives the maximal graph with respect to the $e^{\mathcal{ABC}}$ index of bicyclic graphs of order n. We present several relations between $e^{\mathcal{ABC}}({\rm Y})$ and $ABC({\rm Y})$ of graph ${\rm Y}$. Finally, we provide a conclusion summarizing our findings and discuss potential directions for future research. Full article

Background/Objectives: The classification of psychological disorders has gained significant importance due to recent advancements in signal processing techniques. Traditionally, research in this domain has focused primarily on binary classifications of disorders. This study aims to classify five distinct states, including one control group and four categories of psychological disorders. Methods: Our investigation will utilize algorithms based on Granger causality and local graph structures to improve classification accuracy. Feature extraction from connectivity matrices was performed using local structure graphs. The extracted features were subsequently classified employing K-Nearest Neighbors (KNN), Support Vector Machine (SVM), AdaBoost, and Naïve Bayes classifiers. Results: The KNN classifier demonstrated the highest accuracy in the gamma band for the depression category, achieving an accuracy of 89.36%, a sensitivity of 89.57%, an F1 score of 94.30%, and a precision of 99.90%. Furthermore, the SVM classifier surpassed the other machine learning algorithms when all features were integrated, attaining an accuracy of 89.06%, a sensitivity of 88.97%, an F1 score of 94.16%, and a precision of 100% for the discrimination of depression in the gamma band. Conclusions: The proposed methodology provides a novel approach for analyzing EEG signals and holds potential applications in the classification of psychological disorders. Full article

An edge-coloring $\sigma$ of a connected graph G is called rainbow if there exists a rainbow path connecting any pair of vertices. In contrast, $\sigma$ is monochromatic if there is a monochromatic path between any two vertices. Some graphs can admit a coloring which is simultaneously rainbow and monochromatic; for instance, any coloring of $K_n$ is rainbow and monochromatic. This paper refers to such a coloring as dual coloring. We investigate dual coloring on various graphs and raise some questions about the sufficient conditions for connected graphs to be dual connected. Full article

The impact of disturbances on a transportation network varies depending on the location and characteristics of the affected highway segments. Given limited resources, it is crucial to prioritize the protection and repair of highway segments based on their importance to maintaining overall network performance during disruptions. This paper proposes a novel method for ranking the importance of highway segments, leveraging a novel local–transit percolation and clustering-based method. Initially, the highway network is constructed by Graph theory, and the k-means clustering method is applied considering each segment’s transit and local traffic flows. Subsequently, a local–transit percolation model is constructed to generate an initial ranking of segments based on the size of the second-largest clusters during the percolation phase transition. A secondary ranking is performed by refining the results from the clustering phase. Results of a control experiment show that, compared to baselines, the proposed ranking approach demonstrates a significantly improved ability to sustain network demand and connectivity when high-ranked segments are moved. The model uncertainty analysis was conducted by adding noise to the gantry records, and the experiments demonstrated that the model exhibits robustness under noisy conditions. These findings highlight the effectiveness and superiority of the proposed method. Full article

In this paper, we examine the interplay between the structural and spectral properties of the unit graph $G\left({\mathbb{Z}}_n\right)$ for $n=p_1^{r_1}{p}_2^{r_2}\dots p_k^{r_k}$, where $p_1,p_2,\dots ,p_k$ are distinct primes and $k,r_1,r_2,\dots ,r_k$ are positive integers such that at least one of the $r_i$ must be greater than 1. We first analyze the structure of the unit graph of ${\mathbb{Z}}_n$, treating it as what we will define as a ‘generalized join graph’ under these conditions. We then determine the Laplacian spectrum of $G\left({\mathbb{Z}}_n\right)$ and deduce that it is integral for all n. Consequently, we obtain the Laplacian spectral radius and algebraic connectivity of $G\left({\mathbb{Z}}_n\right)$. We also prove that the vertex connectivity of $G\left({\mathbb{Z}}_{pq}\right)$ is $(p-2)q$, where $2\ne p<q$. We deduce the vertex connectivity of $G\left({\mathbb{Z}}_n\right)$ when $n=p^r{q}^s$, where $2\ne p<q$ are primes and $r,s$ are positive integers. Finally, we present conjectures regarding the vertex connectivity of $G\left({\mathbb{Z}}_n\right)$ when $n=p_1{p}_2\dots p_k$ and $n=p_1^{r_1}{p}_2^{r_2}\dots p_k^{r_k}$, where $p_i$ are distinct primes, $r_i$ are positive integers, and $1\le i\le k$. Full article