Graph Connectivity Research Articles

Cutting Barnette graphs perfectly is hard

A perfect matching cut is a perfect matching that is also a cutset, or equivalently, a perfect matching containing an even number of edges on every cycle. The corresponding algorithmic problem, Perfect Matching Cut, is known to be NP-complete in subcubic bipartite graphs [Le & Telle, TCS '22], but its complexity was open in planar graphs and cubic graphs. We settle both questions simultaneously by showing that Perfect Matching Cut is NP-complete in 3-connected cubic bipartite planar graphs or Barnette graphs. Prior to our work, among problems whose input is solely an undirected graph, only Distance-2 4-Coloring was known to be NP-complete in Barnette graphs. Notably, Hamiltonian Cycle would only join this private club if Barnette's conjecture were refuted.

Critical-edge based tabu search algorithm for solving large-scale multi-vehicle Chinese postman problem

The min–max multi-vehicle Chinese postman problem is an NP-hard problem, which is widely used in path planning problems based on road network graphs, such as urban road structure probing planning, urban road underground cavity detection planning, high-voltage line inspection planning, and so on. With the rapid increase in the number of nodes and connections of road network graph, the solution time and path equilibrium constraints pose new challenges to the problem solving. In this paper, we propose a critical-edge tabu search algorithm, CTA-kroutes, for solving the min–max multi-vehicle postman problem for large-scale road networks. First, the initial solution with balanced path lengths is obtained by segmenting the Eulerian paths; second, the critical edges are moved in the initial solution to construct the neighborhood solution, and the tabu search algorithm is used to find the optimal solution iteratively; and lastly, the solution optimization algorithm is used at the end of each iteration to de-duplicate and optimally reconstruct the current search result. Experiments show that the CTA-kroutes algorithm can effectively improve the equalization of multi-vehicle paths and its applicability to large-scale road networks.

On Querying Historical Connectivity in Temporal Graphs

We study the historical connectivity query in temporal graphs where edges continuously arrive. Given an arbitrary time window, and two query vertices, the problem aims to identify if two vertices are connected by a path in the snapshot of the window. The state-of-the-art method designs an index based on the two-hop cover, and updating the index is costly when new edges arrive. In this paper, we propose a new framework and design a novel forest-based index for historical connectivity queries. The index enables us to answer queries by searching if two vertices are connected in the forest. We update the index by modifying a forest structure. Our techniques also work for connectivity query processing in a sliding window of temporal graphs. Extensive experiments have been conducted to show the considerable advantages of our approach compared with the state-of-the-art methods in both historical connectivity queries and sliding-window connectivity queries.

Factors of HOMFLY polynomials

We study factorizations of HOMFLY polynomials of certain prime knots and oriented links. We begin with a computer analysis of prime knots with at most 12 crossings, finding 17 non-trivial factorizations. Next, we give an irreducibility criterion for HOMFLY polynomials of oriented links associated to 2-connected plane graphs.

ON THE LOCATING CHROMATIC NUMBER OF DISJOINT UNION OF BUCKMINSTERFULLERENE GRAPHS

Let be a connected non-trivial graph. Let c be a proper vertex-coloring using k colors, namely . Let be a partition of induced by , where is the color class that receives the color . The color code, denoted by , is defined as , where for , and is the distance between two vertices and in G. If all vertices in have different color codes, then is called as the locating-chromatic -coloring of . The locating-chromatic number of , denoted by , is the minimum such that has a locating coloring. Let be the Buckminsterfullerene graph on vertices. Buckminsterfullerene graph is a 3-connected planar graph and a member of the fullerene graphs, representing fullerene molecules in chemistry. In this paper, we determine the locating chromatic number of the disjoint union of Buckminsterfullerene graphs, denoted by .

Integration of Semantic and Topological Structural Similarity Comparison for Entity Alignment without Pre-Training

Entity alignment (EA) is a critical task in integrating diverse knowledge graph (KG) data and plays a central role in data-driven AI applications. Traditional EA approaches rely on entity embeddings, but their effectiveness is limited by scarce KG input data and representation learning techniques. Large language models have shown promise, but face challenges such as high hardware requirements, large model sizes and computational inefficiency, which limit their applicability. To overcome these limitations, we propose an entity-alignment model that compares the similarity between entities by capturing both semantic and topological information to enable the alignment of entities with high similarity. First, we analyze descriptive information to quantify semantic similarity, including individual features such as types and attributes. Then, for topological analysis, we introduce four conditions based on graph connectivity and structural patterns to determine subgraph similarity within three hops of the entity’s neighborhood, thereby improving accuracy. Finally, we integrate semantic and topological similarity using a weighted approach that considers dataset features. Our model requires no pre-training and is designed to be compact and generalizable to different datasets. Experimental results on four standard EA datasets validate the effectiveness of our proposed model.

Spatialities between property and the commons: an interval of tolerance

This paper examines the relations of ‘space’ with ‘property’ and ‘commons’. Property is an exclusionary mechanism that regulates human relationships through space based on ownership, boundary, and control. Contrarily, the commons is a spatial practice of encounter, collaboration, and sharing, open to all kinds of participation of the multitude. With a research methodology grounded in the principle of ‘tolerance’, this study questions the spatialities between property and the commons, with or without coexistence and communication. To achieve this, a diagrammatical method for ‘a theoretical reading over an interval’ is generated, which enables a debate on the property and the commons over a conceptual graph of connections of ‘spatial tendencies’, ‘theoretical structures’, and ‘spatial activism’. The ‘interval of tolerance’ graph reveals the connections as a tolerance environment for encountering differences and ensuring spatial relations. Thus, the expansion of networks of connections means the expansion of tolerance. The study concludes that the interval of tolerance narrows towards property but broadens towards the commons, which means spatial toleration is high in the commons, but low in property.

Local connection reinforcement learning method for efficient robotic peg-in-hole assembly

Traditional robotic peg-in-hole assembly methods rely on complex contact state analysis. Reinforcement learning (RL) is gradually becoming a preferred method of controlling robotic peg-in-hole assembly tasks. However, the training process of RL is quite time-consuming because RL methods are always globally connected, which means all state components are assumed to be the input of policies for all action components, thus increasing action space and state space to be explored. In this paper, we first define continuous space serialized Shapley value (CS3) and construct a connection graph to clarify the correlativity of action components on state components. Then we propose a local connection reinforcement learning (LCRL) method based on the connection graph, which eliminates the influence of irrelevant state components on the selection of action components. The simulation and experiment results demonstrate that the LCRL method can achieve the same average reward as the traditional RL method in only 49% of episodes. In the final episode, the LCRL method's final reward is 35% higher than that of the traditional RL method, which guarantees the rapidity and stability of the assembly process.

Modified Detour Index of Hamiltonian Connected (Laceable) Graphs

Objectives: To explore the bounds for the modified detour index of certain Hamiltonian connected and laceable graphs. Methods: The Wiener index , detour index and the modified detour index are used. Findings: Here we introduce the modified detour index and its least upper bounds for Hamiltonian connected and laceable graphs, by formulating the constraints. Novelty: Based on the modified detour index, the bounds for some special graphs such as: Hamiltonian connected graphs of two families of convex polytopes ( and ) and Hamiltonian laceable graphs of spider graph ( ) and image graph of prism graph ( ) are encountered here. Keywords: Hamiltonian graph, Hamiltonian connected, Hamiltonian laceable, Wiener index, detour index

Evaluating Graph Attention Networks as an Alternative to Transformers for ABSA Task in Low-Resource Languages

Opinions toward subjects and products hold immense relevance in business to guide decision-making processes. However, due to the increase in user-generated content, manual analysis is unrealistic. Techniques such as Sentiment Analysis are paramount to understanding and quantifying human emotion expressed in text data. Aspect-Based Sentiment Analysis aims to extract aspects from an opinionated text while identifying their underlying sentiment. Graph-based text representations have been shown to bring benefits to this task, as they explicitly represent structural relationships in text. While studies have demonstrated the effectiveness of this representation for Aspect-based Sentiment Analysis using Graph Neural Networks in English, there is only sparse evidence of improvement using these techniques for low-resource languages such as Portuguese. We develop a straightforward Graph Attention Network model for the Aspect-Based Sentiment Analysis task in Brazilian Portuguese. The proposed approach achieves a Balanced Accuracy score of 0.74, yielding competitive results and ranking third place in the ABSAPT competition. Furthermore, by leveraging sparse graph connections our model is less computationally demanding than a Transformer architecture in terms of training and inference.

Edges incident with a vertex of degree greater than four and the number of contractible edges in a 4-connected graph

Let G be a 4-connected graph, and let Ec(G) denote the set of 4-contractible edges of G and V≥5(G) denote the set of vertices of G whose degree is greater than 4. Under this notation, we show that |Ec(G)|≥(1/26)∑u∈V≥5(G)degG(u).

BIM-based connectivity graph and voxels classification for pedestrian-hazard interaction

ABSTRACT This paper concentrates on establishing a connectivity graph between building entities to model hazard flow and the interaction between pedestrians and hazards. Although three different ways are explored, the Uniform raycast-based approach resulted in being the most robust. We establish a link between hazards, indoor spaces and pedestrians through voxels, where navigable voxels are first derived, and further classified as IfcSpace and IfcDoor. In the end, only voxels with unique properties are kept, being < 1% of the total number of a building. Once the connectivity graph and voxels are identified the interaction between pedestrians and hazards is presented as straightforward.

On the algebraic connectivity of some token graphs

The k-token graph Fk(G)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F_k(G)$$\\end{document} of a graph G is the graph whose vertices are the k-subsets of vertices from G, two of which are adjacent whenever their symmetric difference is a pair of adjacent vertices in G. It was proved that the algebraic connectivity of Fk(G)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F_k(G)$$\\end{document} equals the algebraic connectivity of G with a proof using random walks and interchange of processes on a weighted graph. However, no algebraic or combinatorial proof is known, and it would be a hit in the area. In this paper, we algebraically prove that the algebraic connectivity of Fk(G)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F_k(G)$$\\end{document} equals the one of G for new infinite families of graphs, such as trees, some graphs with hanging trees, and graphs with minimum degree large enough. Some examples of these families are the following: the cocktail party graph, the complement graph of a cycle, and the complete multipartite graph.

A comparative analysis of constraint and connectivity graph techniques for assembly sequence generation in robotic assembly cells

The paper describes a comparative study on the assortment of appropriate assembly-generating techniques for robotic assembly cells. Several techniques have been developed and tested for the creation of viable sequences. Most of these techniques employ computational techniques to generate assembly sequences. Nevertheless, these techniques rely on a large number of assumptions and use insignificant data during the development of assembly sequences. In the present study, two techniques, viz., the connectivity graph technique and the constraint technique are selected, since they are very general, expedient, and easy to implement. Further, selected techniques can easily be automated to increase the productivity of robotics assembly cell. Each technique was applied to four products with different complexities to check their suitability in the context of robotic assembly cell. In the connectivity graph technique, the disassembly of components begins with the sink node in the connectivity graph and ends when no sink node is available. The constraint technique chooses two constraints: the G-constraint and the C-constraint. The process of disassembling the components starts with a component that does not have any G-constraint and satisfies the C-constraint. The G-constraint checks for geometric interference, and the C-constraint checks for connectivity relationships among the components. Both techniques are automated using C++ programming to obtain rapid and efficient results. The automation of assembly techniques is expected to lead to a revolutionary transformation in the assembly sector. The connectivity graph technique is found to be suitable for the robotic assembly cells as described in this article.

Structure-property modeling of coumarins and coumarin-related compounds in pharmacotherapy of cancer by employing graphical topological indices.

Coumarins, a subgroup of colorless and crystalline oxygenated heterocyclic compounds originally discovered in the plant Dipteryx odorata, were the subject of a recent study investigating their quantitative structure-activity relationship (QSAR) in cancer pharmacotherapy. This study utilized graph theoretical molecular descriptors, also known as topological indices, as a numerical representation method for the chemical structures embedded in molecular graphs. These descriptors, derived from molecular graphs, play a pivotal role in quantitative structure-property relationship (QSPR) analysis. In this paper, intercorrelation between the Balban index, connective eccentric index, eccentricity connectivity index, harmonic index, hyper Zagreb index, first path Zagreb index, second path Zagreb index, Randic index, sum connectivity index, graph energy and Laplacian energy is studied on the set of molecular graphs of coumarins. It is found that the pairs of degree-based indices are highly intercorrelated. The use of these molecular descriptors in structure-boiling point modeling was analyzed. Finally, the curve-linear regression between considered molecular descriptors with physicochemical properties of coumarins and coumarin-related compounds is obtained.

Social policy for the development of educational inclusion in Ukrainian schools: a pedagogical analysis

The main purpose of the article is to formulate an effective policy for the development of inclusiveness in education. For this purpose, the object of research will be school educational institutions in Ukraine. The scientific task will include modeling the most significant educational factors influencing the formation of modern social policy for the development of inclusiveness in school institutions. The research methodology involves the use of graph theory and the connection graph method to identify the most significant impact factors. As a result of the analysis, the two most significant factors influencing the formation of modern social policy for the development of inclusiveness in school institutions were identified. Based on this, the key principles for the formation of modern social policy for the development of inclusiveness in school institutions were presented. The study has a limitation by not taking into account other educational institutions, only schools. Further research should be devoted to exploring the formation of social policies for the development of inclusiveness in universities.

General translation of cellular to shellular polyhedral structures using reciprocity

Shell-based cellular (shellular) funicular structures (SFSs) are single-layer 2-manifold efficient structures with anticlastic curvature, designed in the context of graphic statics. This research proposes a comprehensive methodology for designing these efficient structures in the context of graphic statics. Due to the significant challenges in the process of designing these structures, and the ease of using 3D graphic statics in designing cellular funicular structures, this article proposes a general technique to translate any cellular funicular structure (CFS) to a shellular version (SFS). To address this transition, this study presents an integrated methodology coupled with a computational algorithm. This technique proposes a new tetrahedralization method using the reciprocal relationship between the force and the form diagrams, generalizing the translation technique. As a result, the research explores a spectrum of shellular funicular structures, under pure compression or tension states. Diverse design techniques are introduced, enabling the creation and manipulation of these structures through their three-dimensional spatial connectivity graphs, termed “labyrinths”. A comparison between the structural performance of cellular and shellular funicular structures with similar volume density is performed displaying that for the same boundary condition, a shellular specimen can tolerate forces three times more than a cellular structure. To emphasize the practical utility of this design methodology, the study delves into its application at micro and meso scales. Specifically, it showcases the utilization of the shellular technique in the design of the midsole structure of a sneaker. This innovative approach draws inspiration from the pressure patterns exerted by the soles of the feet, emphasizing the adaptability and versatility of the proposed design technique. The results display that shellular funicular structures, with their lightweight and efficient nature, demonstrate superior structural capacity compared to their cellular counterparts and are applicable across micro, meso, and macro scales.

A note on [formula omitted]-coloring and [formula omitted]-coloring 4-regular graphs

Let ∂H(u) be the set of edges incident with a vertex u in the graph H. We say that a graph G is H-colorable if there exist total functions f:E(G)→E(H) and g:V(G)→V(H) such that f is a proper edge-coloring of G and for each vertex u∈V(G) we have f(∂G(u))=∂H(g(u)). Let X¯ be the graph obtained by adding three parallel edges between two degree one vertices of the graph K1,4. Let Aˆ be the graph obtained by adding two pendant edges to two different vertices of a triangle and then adding two edges between the degree two vertex and the two adjacent degree three vertices. Malnegro and Ozeki (2024) [7] asked whether every 4-regular graph with an even number of vertices and an even cycle decomposition admits an X¯-coloring or an Aˆ-coloring and whether every 2-connected planar 4-regular graph with an even number of vertices admits such a coloring. Additionally, they conjectured that for every 2-edge-connected simple cubic graph G with an even number of edges, the line graph L(G) is X¯-colorable. In this short note, we discuss two algorithms for deciding whether a graph G is H-colorable. We give negative answers to the two questions and disprove the conjecture by finding suitable graphs, as verified by two independent algorithms.

A Metro Passenger Flow Forecasting Model Based On Time-series Evolving Interaction Graph Network

Passenger flow forecasting is an important task in metro operation management. In order to achieve more accurate metro passenger flow forecasting, this paper proposes a metro passenger flow forecasting model based on time-series evolution interaction graph. First, by introducing two kinds of inter-station interaction graphs, namely connectivity graph and temporal correlation graph, to capture the potential interaction relationship among metro passenger flow stations. Then, by using the time-series evolving graph, the weights of the graph convolutional neural network are dynamically evolved in time series. Finally, taking Suzhou Metro as an example, the short-term passenger flow of the metro is forecasted. The experimental results show that the Root Mean Squared Error (RMSE) of this model is 34.17, the Mean Absolute Error (MAE) is 16.35, the R-Squared is 0.94, the Mean Absolute Percent Error (MAPE) is 0.21. All evaluation metrics are better than the baseline models, thus verifying the effectiveness and applicability of the metro passenger flow forecasting model based on the time series evolution interaction graph.

A connectivity index based on adjacent vertices in cubic fuzzy graph with an application

A cubic fuzzy graph is a type of fuzzy graph that simultaneously supports two different fuzzy memberships. The study of connectivity in cubic fuzzy graph is an interesting and challenging topic. This research generalized the neighborhood connectivity index in a cubic fuzzy graph with the aim of investigating the connection status of nodes with respect to adjacent vertices. In this survey, the neighborhood connectivity index was introduced in the form of two numerical and distance values. Some characteristics of the neighborhood connectivity index were investigated in cubic fuzzy cycles, saturated cubic fuzzy cycle, complete cubic fuzzy graph and complementary cubic fuzzy graph. The method of constructing a cubic fuzzy graph with arbitrary neighborhood connectivity index was the other point in this research. The results showed that the neighborhood connectivity index depends on the potential of nodes and the number of neighboring nodes. This research was conducted on the Central Bank’s data regarding inter-bank relations and its results were compared in terms of neighborhood connectivity index.