# Energy-Efficient Edge Optimization Embedded System Using Graph Theory with 2-Tiered Security
## 1 Introduction  
Due to an emerging networking environment, the number of users and applications is growing exponentially. The traffic of data going through the base station also increases as the number of users increases. Device-to-device (D2D) communication is seen as one of the best ways to reduce the chance of cellular users losing service in 5G [1, 2, 3]. The cellular licensed band can be used for D2D communication in an underlay or an overlay mode [4, 5]. Integrating sensors, embedded computing, and communication technologies are known as the Internet of Things (IoT). The IoT is designed to provide seamless services to everything, at any time, everywhere. After the internet and information and communication technology, IoT technologies play a critical role everywhere, especially in developing smart systems [6, 7, 8]. Accordingly, to researchers and the community, IoT will have a greater influence on society than the internet and information and communication technologies, which will benefit both sectors and society [9, 10, 11]. The usage of a prospective IoT system allows common system-level design challenges such as energy efficiency, robustness, scalability, interoperability, and security concerns to be addressed. A high degree of physical security is essential forwireless communications in the IoT to complement conventional security measures used at high levels since IoT is anticipated to convey significant and private information [12; 13].  
On the other hand, edge computing is a standard evolving to meet the rising networking needs from end devices to intelligent objects [14; 15]. For reduced latency, increased security, and privacy, edge computing enables the processing to be offloaded from cloud data centers to the network edge and edge nodes [16; 17]. However, due to the complex relationships between edge devices, edge servers, and cloud data centers, energy efficiency in edge computing has received far less attention than it has in cloud data centers. Much research has investigated the development of the optimizing system with the support of artificial intelligence [18; 19]. They increased energy efficiency with improved data delivery, but it is still a hot problem and needs more attention. The proposed solution should be able to impose the least overhead on low-powered devices and avoid unnecessary data transferring.  
The proposed system provides the main contributions as follows:  
1. It proposes an intelligent method for extracting minimal spanning trees using theory.
2. The cost function is optimized using real-time parameters and, accordingly, end-to-end routes are identified.
3. It provides security on two main entrance points: from the IoT system to edge devices and from edge devices to mobile sinks. Such tiers protect against network threats and increase the reliability of the nodes.
4. The proposed system is tested and validated in its performance in terms of resource management and energy efficiency.  
The rest of the paper is organized in the following subsections. Section 2 presents the related work. Section 3 highlights the problem statement. Section 4 explains the overview of the proposed system with all its components. In Section 5, the simulation environment is explained, and in Section 6, experimental results and discussions are provided. Finally, Section 7 ends this research work with future directions.