## 1 Introduction  
A Wireless Sensor Network (WSN) constitutes several sensor nodes (or simply nodes) forming a network amongst themselves and sensing information from their surrounding environment. The sensed information will be transmitted to a data collection point known as sink node or Base Station (BS) [1]. The sensed information is typically environmental parameters such as temperature, pH values of soil, etc., depending upon the type of the applications [2, 3]. The data collected at the BS are interpreted for any abnormal activities, and accordingly, suitable measures will be taken. WSN has various applications such as habitat monitoring, volcanic eruption monitoring, landslide detections, and many more. To quote an example of a specific application, [PERSON] et al. in [4] have developed a wireless sensor system for monitoring harsh environments such as nuclear storage facilities. Research in WSNs is not just limited to routing protocol design, but other sub-areas such as battery-free communication and underwater sensor communication are also extensively explored [5]. In WSN, every node is equipped with a battery and a husky computational processor. The activities performed by nodes such as data sensing, reception, and transmission consume some energy. The battery power keeps on depleting due to such activities, and ultimately, the battery is exhausted. As WSNs are deployed in mission-critical applications, it is practically impossible to replace the battery of the nodes after the battery power is completely drained [6]. Hence, the majority of the research work on WSN focuses on efficient utilization. The network's energy consumption could be effectively prolonged through better deployment strategies, data aggregation schemes, designing efficient routing protocols, and many more [7]. Routing protocol design has attracted many researchers of the WSN community, and it has been found that cluster-based routing protocols have proven to provide promising expected results. Cluster-based routing strategies are further mentioned in [1,7,8]. Network lifetime improvement is the primary design goal of WSNs. Clustering and routing have been the two most preferred network lifetime enhancement methods for WSNs [9, 10, 11, 12]. Clustering is a process where the most eligible sensor node is designated as cluster head, which will ensure energy-efficient data aggregation and transmission among the member nodes. The challenges lie in selecting such a suitable node as a cluster head, resulting in network life prolongation. The idea behind selecting a cluster head node is to reduce the data transmission distance, as it is directly proportional to the energy consumption pattern of the nodes. Some routing and clustering methods showcase single-hop and multi-hop communication architectures for achieving the energy efficiency of the network. In single-hop communication, cluster heads are expected to send the data directly to the sink node. In contrast, in multi-hop communication, cluster heads can transmit data via other cluster head nodes to the sink node. The choice of communication, i.e., either single-hop or multi-hop, largely depends upon the number of nodes. Ideally, if the number of nodes in the network is large, then multi-hop communication is suitable. Though the clustering approach has its benefits, ensuring cluster quality is a challenge [13]. Cluster quality can be measured with respect to inter-cluster and intra-cluster distances [14,15]. The general thought is that clusters need to be separated enough; i.e., the inter-cluster distance should be sufficient so that clusters are formed to cover the entire network. If clusters formed are very close to one another, there is a possibility of overlapping cluster zones. Therefore, if there is a possibility of separating clusters in a balanced manner, it can avoid problems of overlapping cluster zones and insufficient network coverage.