Square difference labeling and co-secure domination in middle graph of certain graphs

Cascading failures of loads in isolated networks under random failures or intentional attacks have been studied in the past decade. The corresponding results for interconnected networks remain missing. In this paper we extend the cascading failure model used in isolated networks to the case of interconnected networks, and study cascades of failures in a data-packet transport scenario. We find that for sparse coupling, enhancing the coupling probability can make interconnected networks more robust against intentional attacks, but keeping increasing the coupling probability has the opposite effect for dense coupling. Additionally, the optimal coupling probability is largely affected by the coupling preference. Finally, assortative coupling is more helpful to resist the cascades compared to disassortative or random coupling. These results can be useful for the design and optimization of interconnected networks such as communication networks, power grids and transportation systems.

This study develops a multi-country model of trade that captures the role of country-specific communications networks interconnectivity, which enhances trade in intermediate business services.The number of countries connected to internationally interconnected networks is found to determine the structure of comparative advantage.That is, countries with interconnected networks have a comparative advantage in the goods that require business services provided via networks.In connected countries, producers of that goods benefit from the efficient transmission of business services.This research also demonstrates that countries whose country-specific networks are not connected to the interconnected networks may become worse off as the result of trade.

<abstract><p>Graph labeling is a source of valuable mathematical models for an extensive range of applications in technologies (communication networks, cryptography, astronomy, data security, various coding theory problems). An edge $ \; \delta - $ graceful labeling of a graph $ G $ with $ p\; $ vertices and $ q\; $ edges, for any positive integer $ \; \delta $, is a bijective $ \; f\; $ from the set of edge $ \; E(G)\; $ to the set of positive integers $ \; \{ \delta, \; 2 \delta, \; 3 \delta, \; \cdots\; , \; q\delta\; \} $ such that all the vertex labels $ \; f^{\ast} [V(G)] $, given by: $ f^{\ast}(u) = (\sum\nolimits_{uv \in E(G)} f(uv)\; )\; mod\; (\delta \; k) $, where $ k = max (p, q) $, are pairwise distinct. In this paper, we show the existence of an edge $ \; \delta- $ graceful labeling, for any positive integer $ \; \delta $, for the following graphs: the splitting graphs of the cycle, fan, and crown, the shadow graphs of the path, cycle, and fan graph, the middle graphs and the total graphs of the path, cycle, and crown. Finally, we display the existence of an edge $ \; \delta- $ graceful labeling, for the twig and snail graphs.</p></abstract>

The Internet of Things (IoT) technology requires low latency communications. One of the lightweight protocols in the IoT is the MQTT protocol. However, the MQTT protocol is not equipped with the appropriate security mechanism. As a consequence, the MQTT messages are easily eavesdropped and modified by the attackers. This research studies the use of AES cryptography-based communication scheme against the TLS-based communication scheme, which can be used to create end-to-end secure communication channels from the MQTT publishers to the MQTT subscribers. Experimental results show that the TLS-based communication scheme possess the highest cost in terms of communication delay and network cost among all schemes in the experiment. Eventually, the AES-based MQTT communication scheme is more appropriate for IoT environments because of its communication delay and network cost, which are considerably equal to the plaintext-based MQTT communications.

L(h,k) Labeling in graph came into existence as a solution to frequency assignment problem. To reduce interference a frequency in the form of non negative integers is assigned to each radio or TV transmitters located at various places. After L(h,k) labeling, L(h,k, j) labeling is introduced to reduce noise in the communication network. We investigated the graph obtained by Cartesian Product betweenCompleteBipartiteGraphwithPathandCycle,i. e.,Km,n×Pr andKm,n×Cr byapplying L(3,2,1)Labeling. The L(3,2,1) Labeling of a graph G is the difference between the highest and the lowest labels used in L(3,2,1) and is denoted by λ3,2,1(G) In this paper we have designed three suitable algorithms to label the graphs Km,n × Pr and Km,n × Cr . We have also analyzed the time complexity of each algorithm with illustration.

Problem statement: A class of dynamic interconnection networks is Multistage Interconnection Networks (MINs) that connects input devices to output devices through a number of switch stages. MINs have assumed importance in recent years; because of their cost-effectiveness. Optical MINs are one type of MINs that have large transmission capacity in the communication networks. There is a major problem in Optical MIN that is crosstalk, which is caused by coupling two signals within a switching element. Approach: To avoid crosstalk in Optical MINs many algorithms have been proposed by many researchers that we review applying five routing algorithms and scheduling them in the Optical MINs. Results: The comparative results of routing algorithms show affective of avoiding crosstalk in number of passes and execution time for different algorithm. Conclusion: The challenge between these routing algorithms is thoroughly investigated, by applying them on Optical MIN and showing which algorithm has better performance to avoid crosstalk.

Fat-tree topologies have been widely adopted as the communication network in data centers in the past decade. Nowadays, high-performance computing (HPC) system designers are considering using fat-tree as the interconnection network for the next generation supercomputers. For extreme-scale computing systems like the data centers and supercomputers, the performance is highly dependent on the interconnection networks. In this paper, we present FatTreeSim, a PDES-based toolkit consisting of a highly scalable fat-tree network model, with the goal of better understanding the design constraints of fat-tree networking architectures in data centers and HPC systems, as well as evaluating the applications running on top of the network. FatTreeSim is designed to model and simulate large-scale fat-tree networks up to millions of nodes with protocol-level fidelity. We have conducted extensive experiments to validate and demonstrate the accuracy, scalability and usability of FatTreeSim. On Argonne Leadership Computing Facility's Blue Gene/Q system, Mira, FatTreeSim is capable of achieving a peak event rate of 305 M/s for a 524,288-node fat-tree model with a total of 567 billion committed events. The strong scaling experiments use up to 32,768 cores and show a near linear scalability. Comparing with a small-scale physical system in Emulab, FatTreeSim can accurately model the latency in the same fat-tree network with less than 10% error rate for most cases. Finally, we demonstrate FatTreeSim's usability through a case study in which FatTreeSim serves as the network module of the YARNsim system, and the error rates for all test cases are less than 13.7%.

ABSTRACTThe integration of unmanned aerial vehicles (UAVs) into cellular networks has emerged as a promising solution to enhance connectivity and service quality in both urban and remote areas. In this paper, we propose a comprehensive framework that combines multi‐agent deep learning with backhaul traffic optimization to effectively manage resources in UAV‐enabled communication networks. By leveraging the capabilities of intelligent reflecting surfaces (IRS) and cell‐free communication strategies, our approach aims to optimize backhaul traffic, ensuring seamless data transmission and improved network throughput. Our methodology involves a dynamic resource allocation mechanism that utilizes multi‐agent deep learning to accurately predict network demands and adaptively allocate resources. The process begins with the collection of real‐time network data, including user demand, traffic patterns, and UAV positions. This data is then fed into a deep learning model, where multiple agents collaboratively analyze and predict future network requirements. Based on the predictions, the resource allocation mechanism dynamically adjusts the distribution of resources, such as bandwidth and power, to meet the anticipated demand. This adaptive strategy enables the network to efficiently handle varying traffic loads, reducing congestion and latency. Furthermore, our backhaul traffic optimization technique focuses on minimizing the energy consumption of UAVs while maximizing their coverage and connectivity. By optimizing the flight paths and altitudes of UAVs, we ensure that they provide optimal coverage with minimal energy expenditure. Additionally, the IRS‐assisted communication further enhances signal quality, reducing the need for high‐power transmissions and thus conserving energy. Our simulations show that our framework improves network throughput, energy efficiency, and reliability. It offers a promising way to manage resources in future UAV‐enabled communication networks.

Current military communication network is a generation old and is no longer effective in meeting the emerging requirements imposed by the future embedded military applications. Therefore, a new interconnection system is needed to overcome these limitations. Two new communication networks based upon Full Duplex Switched Ethernet are presented herein in this aim. The first one uses a distributed communication scheme where equipments can emit their data simultaneously, which clearly improves system's throughput and flexibility. However, migrating all existing applications into a compliant form could be an expensive step. To avoid this process, the second proposal consists in keeping the current centralized communication scheme. Our objective is to assess and compare the real time guarantees that each proposal can offer. The paper includes the functional description of each proposed communication network and a military avionic application to highlight proposals ability to support the required time constrained communications.

Graph labeling is the assignment of integers to edges or vertices or both depending on some factors which is consequential in the field of graph theory. In this paper, anti-magic graph labeling of two graphs, middle graph and total graph of path graph have been mainly focused. Modified proofs of theorems on anti-magic graph labeling have been introduced here. Both of the theorems are applicable for strong anti-magic graph. The correctness of the proofs has been demonstrated through various examples.

High-speed routers and high-performance data centers share a common system-level architecture in which multiple processing nodes are connected by an interconnection network for high-speed communications. Load balancing is an important technique for maximizing throughput and minimizing delay of the interconnection network. In this thesis, efficient load balancing schemes are designed and analyzed for next-generation routers and data centers.
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\nIn high-speed router design, two preferred switch architectures are input-queued switch and load-balanced switch. In an input-queued switch, time-domain load balancing can be carried out by an iterative algorithm that schedules packets for sending in different time slots. The complexity of an iterative algorithm increases rapidly with the number of scheduling iterations. To address this problem, a single-iteration scheduling algorithm called D-LQF is designed, in which exhaustive service policy is adopted for reusing the matched input-output pairs in the previous time slots to grow the match size. 
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\nUnlike an input-queued switch, a load-balanced switch consists of two stages of crossbar switch fabrics, where load balancing is carried out in both time and space domains. Among various load-balanced switches, the feedback-based switch gives the best delay-throughput performance. In this thesis, the feedback-based switch is enhanced in three aspects. Firstly, we focus on reducing its switch fabric complexity. Instead of using crossbars, a dual-banyan network is proposed. The complexity of dual-banyan can be further reduced by merging the two banyans to form a Clos network, resulting in a Clos-banyan network. Secondly, we target at improving the delay performance of the feedback-based switch. A Clos-feedback switch architecture is devised where each switch module in the Clos network is a small feedback-based switch. With application-flow based load balancing, packet order is ensured and the average packet delay is reduced from O(N) to O(n), where N and n are the switch and switch module sizes, respectively. Thirdly, we extend the feedback-based switch to support multicast traffic. Based on the notion of pointer-based multicast VOQ, an efficient multicast scheduling algorithm with packet replication at the middle-stage ports only is proposed. In order to provide close-to-100% throughput for any admissible multicast traffic patterns, a three-stage implementation of feedback-based switch is also designed.
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\nIn designing load balancing schemes for data centers, we focus on the most popular fat-tree based data centers. Notably, packet-based load balancing is widely considered infeasible for data centers. This is because the associated packet out-of-order problem will cause unnecessary TCP fast retransmits, and as a result, severely undermine TCP performance. In this thesis, we show that if packet-based load balancing is performed properly, the packet out-of-order problem can be easily addressed by slightly increasing the number of duplicate ACKs required for triggering fast retransmit. Admittedly, in case of a real packet loss, the loss recovery time will be increased. But our simulation results show that such an increase is far less than the reduction in the network queueing delay (due to a better load-balanced network). As compared to a flow-based load balancing scheme, our packet-based scheme consistently provides significantly higher goodput and noticeably smaller delay.

Social networking content is characterized by many different aspects that may be of interest to a researcher (e.g., the terminology used in social networks appearing as some content delivery model). However, from the point of view of communicative expediency, we will be interested in the communicative aspect of the circulation of social networks: content creation, message structuring, a specificity of perception of this message by network members, and features of expansion and growth of content. This article aims to elucidate the interconnection and interdependence of traditional media and social networks. To accomplish this, its objectives are: 1) to identify the commonality and difference of content inherent in traditional media and social networks; 2) to understand the structure of the newest audiences formed as a result of the converged communication product; 3) to formulate features of «design» of social networks with the participation of media. The object of the article is the collaboration between media and social networks. The subject of the article is communication models of such collaboration. The methodology of the study is based on the use of general research methods of studying the specificity of the analysis of social and communication phenomena. For media, the phenomenon of participation in social networks means multiplication: not to be present in any network platform — the problem is not social, but of worldview. We argue that participation in the social network is no longer a matter of mediation between the audience and the media, but direct involvement in the life of the audience, adherence to the globalism factor, profile coordination of content. Platforms such as Twitter or Facebook become communications net works with participating citizens from anywhere on the planet. These platforms transform them into a network of employees who, by becoming the so-called «citizen journalists», collaborate with professional media. Moreover, they become authors creating new forms, modes and ways of mass communication: newest slang, content, meanings and so on. Therefore, the phenomenon of social networks guarantees the participating media a social and communication «multiplication». Such participation drives the needs, opinions, and desires of both network members and the audience as a new journalism mission-focused not on the truth for the audience but on the audience as a factor in evaluating the truth. We conclude that society’s progress cannot be made without the process of transforming the structures of the social-communication system and the relations between the participants within that system. Moreover, this progress should take place not so much in the spheres of production, distribution, and consumption of social-communication products as within the influence of the results of social networking activities on the measurement of the behavior of members of society. It is a kind of «design» of social networks. The role of designers in the design of such social networking design is to contribute to the new communication reality. We introduce the term «social network designers». Those carry out the design, planning, step-by-step steps of implementation and calculation of the effectiveness of social-network projects. They must adapt their way of work to the dynamic conditions of functioning of social networks, dynamically optimize their ability to respond to those new ones created by these dynamics. Keywords: communications, content, journalism, internet, media, social network.

A graph G is an ordered pair of sets G(V, E), where V is a set of vertices and the elements of set E are usually called edges. The concept of graph labeling has recently gained a lot of popularity in the area of graph theory. his popularity is due not only to the mathematical challenges of graph labelings but also to the wide range of applications that graph labeling offer to other brances of science, for instance, x-ray, cryptography, coding theory, circuit design and communication network design. A graph labeling we mean an assignment of integers to elements of a graph such as vertex, edge, and both. Local antimagic of a graph was motivated by Arumugam et al.. Thus, we initiate to developed the concept of local antimagic vertex coloring for subdevided graphs. A graph G called sub-devided if the graph G be the graph obtained by inserting a vertex to each edge of the graph G. Definition the concept local antimagic vertex coloring is f : E(G) → {1, 2, 3…, |E(G)|} if for any two adjacent vertices a 1 and a 2, w(a 1) = w(a 2), where for v ∈ G, , where E(a) and V(a) are respectively the set of edges incident to a. The local antimagic vertex labeling induces a proper vertex coloring of graph G if each vertex a is assigned the color w(a). The minimum colors needed to coloring the vertices in graph G called local antimagic vertex chromatic number, denoted by χla (G). In this paper we study the local antimagic vertex coloring of sub-devided some special graph as follows SFn,m , SSn,m , SWn,m and SFn,m .

A random walk labeling of a graph G is any labeling of G that could have been obtained by performing a random walk on G. Continuing two recent works, we calculate the number of random walk labelings of perfect trees, combs, and double combs, the torus C 2 × Cn , and the graph obtained by connecting three path graphs at their ends.

Crossbars have been considered one of the most standard switching modules in conventional communication networks due to its simplicity in routing algorithm and fabrication regularity. While in programmable on-chip interconnection networks such as the routing networks in field programmable gate arrays (FPGAs), switch boxes are often used for a better tradeoff between routability and area efficiency. Much work has been done on the topology design of switch boxes, e.g. universal switch boxes and hyper-universal switch boxes. However, the layout design of switch boxes tends to be difficult when the topology of switch boxes is less regular. In this paper we revisit the theoretical design aspects of the classic crossbar design schemes and further investigate a new design style, a so called meta-crossbar, which is obtained from a crossbar by adding the least number of switches and direct contacts to achieve the desired optimal routability. We show that a switch box can always be implemented by a meta-crossbar. This means that the layout design of switch boxes can be done almost like crossbars. As a result, we present a hyper-universal meta-crossbar design, and a three level meta-crossbar based interconnection network design, which is capable of routing all group communication requirements.