Set Of Graphs Research Articles

Evolving subgraph matching on temporal graphs

Given a set of query graphs and specified orders between these query graphs, the evolving subgraph matching problem finds all subgraph sets from the temporal graph that not only match the given query graph set but also satisfy the specified orders. This problem motivates many significant application, e.g., social network analysis, financial fraud crimes detection, biological information mining, and so on. To efficiently address this problem, an evolving subgraph matching algorithm based on two key techniques is proposed. First, a memory-efficient index structure called EMI is designed to compactly store all necessary information required for finding all evolving matchings. To make the EMI compact and to construct the EMI efficiently, several techniques, such as four well-designed filters and adaptive filling orders, are proposed. Second, an evolving subgraph matching enumeration method is designed to immediately run on the EMI instead of on the temporal graph. The enumeration method expands evolving matchings in an edge-by-edge manner. Since the EMI is compactly maintained in the main memory and generally smaller than the temporal graph, the enumeration method runs very fast on the EMI. An extensive experimental evaluation has been carried out to evaluate the proposed algorithm. The experimental results show that the enumeration method executed on the EMI is an order of magnitude faster and requires significantly less memory than the baseline algorithms. To the best of our knowledge, there is no prior work on the evolving subgraph matching on temporal graphs.

CAMIG: Concurrency-Aware Live Migration Management of Multiple Virtual Machines in SDN-Enabled Clouds

By integrating Software-Defined Networking and cloud computing, virtualized networking and computing resources can be dynamically reallocated through live migration of Virtual Machines (VMs). Dynamic resource management such as load balancing and energy-saving policies can request multiple migrations when the algorithms are triggered periodically. There exist notable research efforts in dynamic resource management that alleviate single migration overheads, such as single migration time and co-location interference while selecting the potential VMs and migration destinations. However, by neglecting the resource dependency among potential migration requests, the existing solutions of dynamic resource management can result in the Quality of Service (QoS) degradation and Service Level Agreement (SLA) violations during the migration schedule. Therefore, it is essential to integrate both single and multiple migration overheads into VM reallocation planning. In this paper, we propose a concurrency-aware multiple migration selector that operates based on the maximal cliques and independent sets of the resource dependency graph of multiple migration requests. Our proposed method can be integrated with existing dynamic resource management policies. The experimental results demonstrate that our solution efficiently minimizes migration interference and shortens the convergence time of reallocation by maximizing the multiple migration performance while achieving the objective of dynamic resource management.

A linear-time algorithm for minimum k-hop dominating set of a cactus graph

Given a graph G = ( V , E ) and an integer k ≥ 1 , a k - hop dominating set D of G is a subset of V , such that, for every vertex v ∈ V , there exists a node u ∈ D whose distance from v is at most k . A k -hop dominating set of minimum cardinality is called a minimum k -hop dominating set . In this paper, we present a linear-time algorithm that finds a minimum k -hop dominating set in cactus graphs , which improves the O ( n 3 ) -time algorithm of Borradaile and Le (2017). To achieve this, we show that the k -hop dominating set problem for unicyclic graphs reduces to the piercing circular arcs problem , and show a linear-time algorithm for piercing sorted circular arcs, which improves the best known O ( n log n ) -time algorithm.

Forbidden triples generating a finite set of graphs with minimum degree three

For a family H of graphs, a graph G is said to be H -free if G contains no member of H as an induced subgraph. We let G ̃ 3 ( H ) denote the family of connected H -free graphs having minimum degree at least 3. In this paper, we characterize the families H of connected graphs with | H | = 3 such that G ̃ 3 ( H ) is a finite family, except for the case where { K 3 , K 2 , 2 } ⊆ H . Our results give a fast algorithm determining the chromatic number of several classes of graphs with a forbidden subgraph condition imposed on.

Spanning tree enumeration and nearly triangular graph Laplacians

We present new short proofs of known spanning tree enumeration formulae for threshold and Ferrers graphs by showing that the Laplacian matrices of such graphs admit triangular rank-one perturbations. We then characterize the set of graphs whose Laplacian matrices admit triangular rank-one perturbations as the class of special 2-threshold graphs and introduce a new spanning tree enumeration formula that generalizes the aforementioned formulae for threshold and Ferrers graphs. Our approach includes a new characterization of special 2-threshold graphs that generalizes the characterization of threshold graphs in terms of isolated and dominating vertices. We consider both weighted and unweighted spanning tree enumeration.

Structure of Projective Planar Subgraphs of the Graph Obstructions for Fixed Surface

Consider the problem of studying the metric properties of a subgraph G\v, where v is an arbitrary vertex of obstruction graphs G of a nonorientable genus, which will determine the sets of points of attachment of one subgraph to another and allow constructing prototypes of graphs-obstruction with number of vertices greater than 10 nonorientable genus greater than 1. This problem is related to Erdosh's hypothesis [3] on the coverage of obstruction graphs of an undirected surface of the genus k, where k > 0, the smallest inclusion of the set of k + 1st graph of the homeomorphic K5, or K3,3, in [4] constructively proved for 35 minors of obstruction graphs of the projective plane, a set of 62 with no more than 10 vertices of obstruction graphs and their splits for the Klein surface, as well as some obstruction graphs for other surfaces. In [5], the existence of a finite set of obstruction graphs for a non-orienting surface was proved. A similar problem was considered in [6], where models or prototypes of obstruction graphs were considered. The prototype of the graph-obstruction of the undirected genus, we will call the graphs that have their own subgraph graph-obstruction of the undirected genus. In [7, 8] the tangent problem of covering the set of vertices with the smallest number of cycles-boundaries of 2-cells was considered, the concept of cell distance is given in [9, 10], where the boundaries of an oriented genus of graphs formed from planar graphs and a simple star glued to some of its peaks. Hypothetically, it is possible to obtain them by recursive φ-transformation of the graph-obstruction of the projective plane and a copy of its planar subgraph given on vertices, edges or parts of edges, or simple chains, i.e. achievable parts of the so-called graph-basis (graph of homeomorphic graph Kuratovsky plane). We assume that instead of one subgraph there can be several copies of subgraphs of graphs-obstructions of the projective plane.The article has an introduction and two parts, in which the structural properties of subgraphs of obstruction graphs for an undirected surface, presented as a φ-image of one of the Kuratovsky graphs and at least one planar graph, are investigated. The metric properties of the minimal embeddings of the subgraphs of the obstruction graphs for undirected surfaces are considered, and the main result is Theorems 1, 2, and Lemma 3 as the basis of the prototype construction algorithm. Keywords: φ-transformation of graphs, nonorientable surface, prototypes of graph-obstruction.

Crystal structure of 2,5-di-hydroxy-terephthalic acid from powder diffraction data.

The crystal structure of anhydrous 2,5-dhy-droxy-terephthalic acid, C8H6O6, was solved and refined using laboratory X-ray powder diffraction data, and optimized using density functional techniques. The published structure of 2,5-di-hydroxy-terephthalic acid dihydrate was also optimized. The carb-oxy-lic acid groups form strong hydrogen bonds, which form centrosymmetric rings with graph set R 2 2(8). These hydrogen bonds link the mol-ecules into chains along [011]. There is an intra-molecular O-H⋯O hydrogen bond between the hydroxyl group and the carbonyl group of the carb-oxy-lic acid. The hydrogen bonding in the dihydrate is very different. Although the intra-molecular hy-droxy/carb-oxy-lic acid hydrogen bond is present, the water mol-ecule acts as an acceptor to the carb-oxy-lic acid and a donor to two other oxygen atoms. The carb-oxy-lic acid groups do not inter-act with each other directly.

Thermal micropolar and couple stresses effects on peristaltic flow of biviscosity nanofluid through a porous medium

The main aim of the current study is to analyze couple stresses effects on MHD peristaltic transport of a micropolar non-Newtonian nanofluid. The fluid flows through a porous media between two horizontal co-axial tubes. The effects of radiation, chemical reaction, viscous and ohmic dissipation are considered. The inner tube is solid and uniform, while the outer tube has a sinusoidal wave traveling down its wall. The governing equations have been simplified using low-Reynolds number and long wave-length approximations, thus a semi-analytical solutions have been obtained using the homotopy perturbation method. Numerical results for the behaviors of the axial velocity, microrotation velocity, temperature and nanoparticles concentration with the physical parameters are depicted graphically through a set of graphs. Furthermore, the values of the skin friction coefficient, Nusselt and nano Sherwood numbers are computed and presented graphically through some draws. Moreover, the trapping phenomenon is discussed throughout a set of figures. The present study is very important in many medical applications, as the gastric juice motion in the small intestine when an endoscope is inserted through it. Further, gold nanoparticles are utilized in the remedy of cancer tumor.

Identifying the Exact Value of the Metric Dimension and Edge Dimension of Unicyclic Graphs

Given a simple connected graph G, the metric dimension dim(G) (and edge metric dimension edim(G)) is defined as the cardinality of a smallest vertex subset S⊆V(G) for which every two distinct vertices (and edges) in G have distinct distances to a vertex of S. It is an interesting topic to discuss the relation between these two dimensions for some class of graphs. This paper settles two open problems on this topic for unicyclic graphs. We recently learned that Sedlar and Škrekovski settled these problems, but our work presents the results in a completely different way. By introducing four classes of subgraphs, we characterize the structure of a unicyclic graph G such that dim(G) and edim(G) are equal to the cardinality of any minimum branch-resolving set for unicyclic graphs. This generates an approach to determine the exact value of the metric dimension (and edge metric dimension) for a unicyclic graph.

The feasible region of induced graphs

The feasible region Ωind(F) of a graph F is the collection of points (x,y) in the unit square such that there exists a sequence of graphs whose edge densities approach x and whose induced F-densities approach y. A complete description of Ωind(F) is not known for any F with at least four vertices that is not a clique or an independent set. The feasible region provides a lot of combinatorial information about F. For example, the supremum of y over all (x,y)∈Ωind(F) is the inducibility of F and Ωind(Kr) yields the Kruskal-Katona and clique density theorems.We begin a systematic study of Ωind(F) by proving some general statements about the shape of Ωind(F) and giving results for some specific graphs F. Many of our theorems apply to the more general setting of quantum graphs. For example, we prove a bound for quantum graphs that generalizes an old result of Bollobás for the number of cliques in a graph with given edge density. We also consider the problems of determining Ωind(F) when F=Kr−, F is a star, or F is a complete bipartite graph. In the case of Kr− our results sharpen those predicted by the edge-statistics conjecture of Alon et al. while also extending a theorem of Hirst for K4− that was proved using computer aided techniques and flag algebras. The case of the 4-cycle seems particularly interesting and we conjecture that Ωind(C4) is determined by the solution to the triangle density problem, which has been solved by Razborov.

Peristaltic Transport of Carreau Coupled Stress Nanofluid with Cattaneo-Christov Heat Flux Model Inside a Symmetric Channel

The current analytical study is concerned with studying the impact of Cattaneo-Christov heat flux of an incompressible flow which obeys Carreau nanofluid inside a symmetric channel in the existence of the porous medium. The impacts of couple stress, heat generation absorption, joule heating, couple stress viscous dissipation with Soret as well as Dufour numbers are all presumed. Long wavelength and law Reynold’s number approximations are utilized for solving the governing system of equations. Furthermore, the traditional perturbation method together with the homotopy perturbation technique (HPM) are applied to obtain the resultant solutions of these equations. The different physical parameters on velocity, temperature and nanoparticles concentration distributions are illustrated through a set of graphs. It is found that the elevate in the slip velocity parameter dwindle the velocity. Meanwhile, the rise in the value of thermal relaxation time parameter led to decay the temperature of the fluid. Over and above, enhancing the nano Biot number value caused an enrichment in the concentration of nanofluid.

Parameterized Complexity of Computing Maximum Minimal Blocking and Hitting Sets

A blocking set in a graph G is a subset of vertices that intersects every maximum independent set of G. Let \(\textsf {mmbs} (G)\) be the size of a maximum (inclusion-wise) minimal blocking set of G. This parameter has recently played an important role in the kernelization of Vertex Cover with structural parameterizations. We provide a panorama of the complexity of computing \(\textsf {mmbs} \) parameterized by the natural parameter and the independence number of the input graph. We also consider the closely related parameter \(\textsf {mmhs} \), which is the size of a maximum minimal hitting set of a hypergraph. Finally, we consider the problem of computing \(\textsf {mmbs} \) parameterized by treewidth, especially relevant in the context of kernelization. Since a blocking set intersects every maximum-sized independent set of a given graph and properties involving counting the sizes of arbitrarily large sets are typically non-expressible in monadic second-order logic, its tractability does not seem to follow from Courcelle’s theorem. Our main technical contribution is a fixed-parameter tractable algorithm for this problem.

Investment Decisions under Almost Complete Causal Ignorance

This article investigates investment decision making under conditions of almost complete causal ignorance. Using two basic notions of causal dependence, probabilistic and counterfactual dependence, as building blocks, a formal notion of causal distance is presented that gives decision makers the ability to quantitatively assess the proximity that different causal graphs have to each other. The latter are directed acyclic graphs that can also be used to represent causal relations among economic events. Once the causal distance of each graph in a set of causal graphs is determined, it is possible to select the graph with the shortest total distance to the other graphs. This in turn allows decision makers to select a course of action that will be beneficial regardless of the particular set of causal relations that is actually driving observed economic events. The article describes how causal distance values can be used formally within an optimization to facilitate portfolio construction.

On constant-time quantum annealing and guaranteed approximations for graph optimization problems

Quantum annealing (QA) is a computational framework where a quantum system’s continuous evolution is used to find the global minimum of an objective function over an unstructured search space. It can be seen as a general metaheuristic for optimization problems, including NP-hard ones if we allow an exponentially large running time. While QA is widely studied from a heuristic point of view, little is known about theoretical guarantees on the quality of the solutions obtained in polynomial time. In this paper, we use a technique borrowed from theoretical physics, the Lieb–Robinson (LR) bound, and develop new tools proving that short, constant-time QA guarantees constant factor approximations ratios for some optimization problems when restricted to bounded degree graphs. Informally, on bounded degree graphs the LR bound allows us to retrieve a (relaxed) locality argument, through which the approximation ratio can be deduced by studying subgraphs of bounded radius. We illustrate our tools on problems MaxCut and maximum independent set for cubic graphs, providing explicit approximation ratios and the runtimes needed to obtain them. Our results are of similar flavor to the well-known ones obtained in the different but related QAOA (quantum optimization algorithms) framework.

Chirality for simple graphs of size up to 12

Chirality is one of the important asymmetrical property in wide area of natural science, which has been studied to predict molecular behavior. One of good methods to analyze molecules with complex structures is representing them as graphs embedded in 3-dimensional space. So it is important to study the chirality of spatial graphs to understand structure of chiral molecules. Moreover, Robertson and Seymour’s graph minor theorem implies that a set of minor minimal graphs with respect to intrinsic properties is finite. So it is also important to find a complete set of minor minimal graphs for intrinsic properties. In this paper, we classify minor minimal intrinsically chiral graphs among simple graphs of size up to 12.

Influence of Teaching and Course Evaluation of Performing Arts Students Based on Improved Ant Colony Algorithm and Data Fusion

Teaching quality evaluation plays a very important role in the evaluation of teaching and learning in universities, especially in performing arts courses. Therefore, in this study, the application and detailed analysis process of clustering analysis on student performance data is used to finally obtain the guidance of clustering results on teaching and management. A mathematical model of teachers was established using graph theory to transform the evaluation process into a bipartite graph model and to fully utilize the memory capacity, mastery of prior knowledge, adaptability, and collaboration of the ant colony algorithm. Moving back and forth between the two sets of partial graphs completed the evaluation of the teacher teaching process. In addition, the maximum and minimum pheromone strategies were applied in the original ant colony algorithm; the robustness of the algorithm itself was enhanced by making full use of the memory ability and the necessary prior knowledge mastery in solving the teacher teaching evaluation problem. For the unqualified teachers, according to the principle of PDCA (quality environment), regular training, mutual lectures, and further training can be adopted to improve teachers’ teaching levels. Through comparison, it is found that the general and practical courses of art performance majors do not have professional characteristics, and the professional courses are mostly dance and performance courses, while physical education, sports training, and other related courses are insufficient. Through the method of this study, all students are concentrated in the group of teachers with higher satisfaction, and “teaching” can achieve the expected effect and provide theoretical and practical basis for the development of performing arts courses.

Suppressors of fixation can increase average fitness beyond amplifiers of selection

Evolutionary dynamics on graphs has remarkable features: For example, it has been shown that amplifiers of selection exist that-compared to an unstructured population-increase the fixation probability of advantageous mutations, while they decrease the fixation probability of disadvantageous mutations. So far, the theoretical literature has focused on the case of a single mutant entering a graph-structured population, asking how the graph affects the probability that a mutant takes over a population and the time until this typically happens. For continuously evolving systems, the more relevant case is that mutants constantly arise in an evolving population. Typically, such mutations occur with a small probability during reproduction events. We thus focus on the low mutation rate limit. The probability distribution for the fitness in this process converges to a steady state at long times. Intuitively, amplifiers of selection are expected to increase the population's mean fitness in the steady state. Similarly, suppressors of selection are expected to decrease the population's mean fitness in the steady state. However, we show that another set of graphs, called suppressors of fixation, can attain the highest population mean fitness. The key reason behind this is their ability to efficiently reject deleterious mutants. This illustrates the importance of the deleterious mutant regime for the long-term evolutionary dynamics, something that seems to have been overlooked in the literature so far.

Study on a Strong and Weak n-Connected Total Perfect k-Dominating set in Fuzzy Graphs

In this paper, the concept of a strong n-Connected Total Perfect k-connected total perfect k-dominating set and a weak n-connected total perfect k-dominating set in fuzzy graphs is introduced. In the current work, the triple-connected total perfect dominating set is modified to an n-connected total perfect k-dominating set nctpkD(G) and number γnctpD(G). New definitions are compared with old ones. Strong and weak n-connected total perfect k-dominating set and number of fuzzy graphs are obtained. The results of those fuzzy sets are discussed with the definitions of spanning fuzzy graphs, strong and weak arcs, dominating sets, perfect dominating sets, generalization of triple-connected total perfect dominating sets of fuzzy graphs, complete, connected, bipartite, cut node, tree, bridge and some other new notions of fuzzy graphs which are analyzed with a strong and weak nctpkD(G) set of fuzzy graphs. The order and size of the strong and weak nctpkD(G) fuzzy set are studied. Additionally, a few related theorems and statements are analyzed.

Independence equivalence classes of paths

The independence equivalence class of a graph G is the set of graphs that have the same independence polynomial as G. A graph whose independence equivalence class contains only itself, up to isomorphism, is independence unique. Beaton, Brown and Cameron [2] showed that paths with an odd number of vertices are independence unique and raised the problem of finding the independence equivalence class of paths with an even number of vertices. The problem is completely solved in this paper.

Fuzzy fractional factors in fuzzy graphs

Graph fractional factor theory plays a crucial role in data transmission and network flow existence analysis, and has become one of the hot research branches of graph theory. This paper introduces fuzzy fractional factor in fuzzy graph setting, and an algorithm-based proof of its necessary and sufficient condition is given. The transformation operation is introduced to show that any two fuzzy fractional f $f$ -factors can be converted between each other, and the characteristic of maximum fuzzy fractional factor through increasing walk is determined. Finally, toughness in fuzzy graph setting is introduced, and preliminary toughness bound for fuzzy fractional ι $\iota $ -factor is presented, where ι = min e ∈ E { μ B ( e ) ∣ μ B ( e ) > 0 } $\iota ={\min }_{e\in E}\{{\mu }_{B}(e)| {\mu }_{B}(e)\gt 0\}$ .