## 1 Introduction  
In Wireless Sensor Network (WSN) environments, small, energy-efficient, low-cost sensor nodes are exchanging the sensed data with the base station (BS) effectively [1, 2]. Nowadays, WSNs are considered a new technology issue when machines, humans, and the environment are independently integrated. Consequently, the evolution in memory, processors and microelectronics devices enables the performance of different programmed tasks,in turn allowing sensing and computing elements to be integrated into small devices [3]. Moreover, separated sensors formed WSNs [4; 5] for environmental monitoring or physical conditions, such as temperature, pressure, precision agriculture, sound, machine surveillance, intelligent buildings, facility management, habitat monitoring, preventive maintenance, logistics, and transport, etc. Subsequently, their data bypass via the network to the main location cooperatively [6]. Battlefield supervision as an example of military applications encouraging the development of wireless sensor networks. Today, these networks are used in many manufacturing and consumer applications, such as control and process monitoring, healthcare, and medicines [7; 8; 9], etc. However, energy, distance, and time delay are considered the main challenges of WSN. Furthermore, in most WSN cases, a non-rechargeable battery is used as a sensor power resource. Thus, distances among nodes are highly increasing energy consumption. Accordingly, the cluster-head approach as the core of typical clustering algorithms is used to reduce distances among nodes, decrease service redundancy phenomena, and achieve a balanced distribution for energy consumption. Wrong selection to the cluster head often causes early depletion of the network energy [10]. Additionally, the attackers can gain full control of whole the network, without any need to overtake other nodes, when they gain control of all cluster heads. Conversely, proper cluster head electing may decrease the energy consumption, ensure a constant data flow, increase the data integrity level, and prolong the network lifetime [10]. As is well known, as the distance among nodes and base stations increases, the time delay is increased. Likewise, the CH must be selected in a way that is spatially close enough to the base station as well as the sensor nodes. As a result, the time delay can be reduced effectively, and the speed of the data transmission can be increased accordingly [1]. The excessive calculations for the measuring methods, which are used to ensure the CH election accuracy, and applied by most of the previous studies --especially in stationary networks--such as distance among nodes and base station, signal strength, hop count, node density, have been deliberately ignored. However, the drawbacks of those protocols are the focus on the degree of accuracy in choosing the cluster head by performing complex mathematical operations and measuring multiple factors, causing delays, and draining of the network energy that is supposed to be provided. On the other hand, the LEDCHE-WSN algorithm checks the remaining energy just to ensure that a CH candidate is alive, without adding a burden of calculation and comparison for the remaining energy of the CH candidate with all the other sensor nodes. Instead, good architecture design (known as topology control, see Section 4.1) makes the connectivity more simple and flexible. Furthermore, our proposed architecture is enhanced by using a single-hop model at the cluster core, where it has a small size and a short distance among nodes. Moreover, using a multiple-hop model at the cluster core (as it is in the LEACH protocol) causes multi congestion points in the cluster, which in turn result in quick depletion of the nodes' energy. Therefore, the multi-hop clustering model is used in the cluster edge (between the SN and BS) to achieve good scalability, which the single-hop clustering model does not achieve.