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The communication link in the engineering of Internet of Vehicle (IOV) is more frequent than the communication link in the Mobile ad hoc Network (MANET). Therefore, the highly dynamic network routing reliability problem is a research hotspot to be solved.

The graph theory is used to model the MANET communication diagram on the highway and propose a new reliable routing method for internet of vehicles based on graph theory.

The expanded graph theory can help capture the evolution characteristics of the network topology and predetermine the reliable route to promote quality of service (QoS) in the routing process. The program can find the most reliable route from source to the destination from the MANET graph theory.

The good performance of the proposed method is verified and compared with the related algorithms of the literature.

The European Union (EU) energy supply environment is changing significantly and in a dynamic way, establishing the issue of safe energy imports as main priority. Greece relies heavily on energy imports. Furthermore, Greece aims to be elevated into an energy cross road for the energy supply to the EU. In this respect, the aim of this paper is the investigation of the suitability of graph theory concepts on energy supply networks and its application to represent energy corridors to Greece.

Supporting frameworks to represent and assess the vulnerability of the corridors satisfying the Greek demand in oil and gas are considered a crucial issue and are presented in this paper, based on the graph theory approach. In addition, a pilot application of the shortest path algorithm and the maximum flow at minimum risk algorithm for the oil and gas corridors to Greece is presented and discussed.

This paper introduces the application of graph theory to energy policy analysis. Indeed, the pilot application in oil and gas supply corridors to Greece, although quite simplified, has indicated the applicability of graph theory concepts in such problems and is considered a step forward of the existing studies, supporting the design efforts towards the development of a more reliable energy supply system.

To the best of the authors' knowledge, graph theory's application to energy corridors is not available in the international literature. In this respect, the added value of the paper is the provision of a sufficient decision support framework for the representation and assessment of the energy corridors' risk of energy availability, through the application of graph theory.

Domain decomposition of finite element models (FEM) for parallel computing are often performed using graph theory and algebraic graph theory. This paper aims to present a new method for such decomposition, where a combination of algebraic graph theory and differential equations is employed.

In the present method, a combination of graph theory and differential equations is employed. The proposed method transforms the eigenvalue problem involved in decomposing FEM by the algebraic graph method, into a specific initial value problem of an ordinary differential equation.

The transformation of this paper enables many advanced numerical methods for ordinary differential equations to be used in the computation of the eigenproblems.

Combining two different tools, namely algebraic graph theory and differential equations, results in an efficient and accurate method for decomposing the FEM which is a combinatorial optimization problem. Examples are included to illustrate the efficiency of the present method.

This research will analyze the traditional Iranian buildings according to the climatic factors by the use of graph theory. By this way, the hypothesis that climate factor has a major effect on the organization of the spaces in traditional Iranian buildings will be tested. Access graphs have been used to clarify the connectivity and depth of a building’s spaces from the socio-cultural point of view. However, it cannot be applied to climate studies. Thus, this study developed the existing technique to define building layouts in terms of climate and thermal comfort. The thermal comfort was graphically evaluated by the two main factors like solar gain and wind effect, with the use of a simple multi-attribute rating technique. All the analysis had been done in the interval of zero (the worst condition) to three (the best condition). The proposed orientation-weighted graph method proved that the thermal comfort factors of the buildings under study match the seasonal movements of their inhabitants. Consequently, the developed orientation-weighted graph method can be used to study space organization in traditional Iranian building in terms of solar gain and wind effect.

The authors will review the main concepts of graphs, present the implemented algorithm, as well as explain the different techniques applied to the graph, to achieve an efficient execution of the algorithm, both in terms of the use of multiple cores that the authors have available today, and the use of massive data parallelism through the parallelization of the algorithm, bringing the graph closer to the execution through CUDA on GPUs.

In this work, the authors approach the graphs isomorphism problem, approaching this problem from a point of view very little worked during all this time, the application of parallelism and the high-performance computing (HPC) techniques to the detection of isomorphism between graphs.

Results obtained give compelling reasons to ensure that more in-depth studies on the HPC techniques should be applied in these fields, since gains of up to 722x speedup are achieved in the most favorable scenarios, maintaining an average performance speedup of 454x.

The paper is new and original.

Nodal ordering for the formation of well‐structures stiffness matrices are often performed using graph theory and algebraic graph theory. The purpose of this paper is to present a new method for nodal ordering for profile optimization of finite element models.

In the present method, a combination of graph theory and differential equations is employed. The proposed method transforms the eigenvalue problem involved in optimal ordering of algebraic graph method into a specific initial value problem of an ordinary differential equation.

The transformation of this paper enables many advanced numerical methods for ordinary differential equations to be used in the computation of the eigenproblems.

Combining two different tools, namely graph theory and differential equations, results in a more efficient and accurate method for nodal ordering problem, which is a combinatorial optimization problem. Examples are included to illustrate the efficiency of the present method.

Two important methodologies having some common grounds, but based on differing contexts and paradigms are Physical System Theory (PST) and System Dynamics (SD). The developments in both the fields have taken place almost independently, and attempts have been made to integrate the two to complement their strengths and limitations. This paper provides an overview of PST in terms of its foundations, philosophy, fundamental postulates, recent developments on its simplification and enlargement, and applications to socio‐economic and managerial systems. A comparison of PST is made with SD on different fronts so as to understand their similarities and differences for carving out their place in modelling of managerial and socio‐economic systems and integrating the two more meaningfully and flexibly. The paper is concluded emphasizing the need for a ‘Flexible System Theory’ which can relate many such systems based approaches and techniques on the whole continuum from hard to soft systems thinking to cater the whole spectrum of problem situations effectively.

This paper aims to present a novel approach for assessing the resilience of transportation road infrastructure against different failure scenarios based on the topological properties of the network. The approach is implemented in the context of developing countries where data scarcity is the norm, taking the capital city of Beirut as a case study.

The approach is based on the graph theory concepts and uses spatial data and urban network analysis toolbox to estimate the resilience under random and rank-ordering failure scenarios. The quantitative approach is applied to statistically model the topological graph properties, centralities and appropriate resilience metrics.

The research approach is able to provide a unique insight into the network configuration in terms of resilience against failures. The road network of Beirut, with an average nodal degree of three, turns to act more similarly to a random graph when exposed to failures. Topological parameters, connectivity and density indices of the network decline through disruptions while revealing an entire dependence on the state of nodes. The Beirut random network responds similarly to random and targeted removals. Critical network components are highlighted following the approach.

The approach is limited to an undirected and weighted specific graph of Beirut where the capacity to collect and process the necessary data in such context is limited.

Decision-makers are better able to direct and optimize resources by prioritizing the critical network components, therefore reducing the failure-induced downtime in the functionality.

The resilience of Beirut transportation network is quantified uniquely through graph theory under various node removal modes.

A method for qualitative estimation of reliability of large and complex mechanical and hydraulic systems is presented. It is especially useful for comparison and optimum selection of the structure at the conceptual stage of design when no other information about the salient features or parameters of the system is known. The method permits the identification and analysis of critical paths, loops and subsystems causing failure under different causes and modes. The method is based on graph theory and the graph variants proposed as reliability measures are also modified to yield realistic and useful results. The concept of system graph introduced in the article for dealing with large systems appears to be the most appropriate for analysis, comparison, selection and reliability estimates at the beginning of the system′s design.

This paper proposes a bar‐system graph representation for structural topology optimization using a genetic algorithm (GA).

Based on graph theory, a graph is first used to represent a skeletal structure consisting of joining paths in the design domain, each of which is represented by a chain subgraph with finite number of vertices. Based on the edges of this graph, a bar‐system representation is proposed to define all the bars and the resulting topology is obtained by mapping each bar with its corresponding thickness to the design domain which is discretized into a regular mesh. The design variables are thus reduced to the spatial distribution of the vertices and the thickness of each bar. This method combines the advantages of both continuum and ground structure optimization methods.

The overall procedure is applied to classical structural topology optimization problems and its good performance is illustrated in the numerical examples.

It is suggested that the present representation method is both physically meaningful and computationally effective in the framework of topological optimum design using GAs.