In the graph G (V, E) of UAV networks, also known as UANETs, the collection of UAVs in the network is referred to as V, and the communication links between them as E. Each node in our homogeneous network has a fixed transmission range. An edge occurs between two nodes if their distance is less than their transmission range. A node is capable of locating itself via the Global Positioning System (GPS) or any other system. Table 1 contains a list of the symbols used in our work.

The related definitions are given below:

Definition 1: Relay(u) For a node ∀u ∈ V in a graph G = (V, E), Relay(u) = {v|v ∈ N₁(u)} such that N₂(u) = S_{x∈ Relay(u)}N₁(x)

Definition 2: Connected Dominating Set (CDS) A set S ⊆ V is referred to as Dominating Set (DS) if, given a connected and undirected graph G = (V, E), ∀v ∈ V either v ∈ S or ∃x ∈ N₁(v) with x ∈ S, (i.e., V = U_x∈S N₁(x) ). If the graph that S produces is connected, it is referred to as CDS.

UAVNet is represented by the edge-weighed, connected, and undirected graph G = (V, E, W). The problem can be modeled using the edge weight function W : E → R⁺, where V = {v₁, v₂, ..., v_n} denotes the set of nodes of UANET, E = {(v_i , v_j) | i ≤ n, j ≤ n} ⊆ V × V denotes the communication links between the nodes, and W = {w(i, j) | ∀(v_i , v_j) ∈ E} denotes the set of weights associated with the communication links.

The rest of the article is structured as follows: Section 2 presents the relevant works. Section 3 presents the contributions of the proposed research. The S-ELHR protocol is explained in Section 4. The simulation's findings are shown in section 5. Section 6 represents the work’s conclusion.

The Bounded Diameter Minimum Spanning Tree (BDMST) problem is given as a learning automata-based distributed approach to creating a virtual backbone [25–27]. For quick and effective broadcasting in urban settings, a minimal-size CDS construction technique based on node velocity is proposed. This CDS’ primary function is to lessen the lag in VANET setups. The low stability metric is used to choose the nodes for CDS [22]. Nodes with a higher degree and fewer link modifications were given preference for forming CDS [28]. A stable dominating set construction based on link stability is suggested [23]. If the received beacon signal intensity is less than a threshold, a link is considered weak. To create a stable CDS, nodes with strong connections are found. In UANETs, a framework for backbone stability is established. Their model makes use of the dynamics of node movements, improving network stability for UAVs by taking connection information into account. The backbone creation algorithm favours sign control, total control of incidence, and incidence control over all other factors [29]. For both static and dynamic situations, a CDS construction technique is put forth [30]. In a dynamic setting, a brand-new heuristic called CDS-Hex is suggested [31]. Three metrics—mobility speed, degree, and energy—have been employed in an MPR-based method to build a stable CDS that is energy efficient. For MPR nodes with transmission power, battery power, degree, and mobility, a weight-based screening method has been proposed [32].

For the purpose of maintaining connectivity among the drone horde in applications for transportation during disasters, a CDS has been implemented. A node with a higher priority has been chosen for CDS [27,33,34]. For effective connectivity and maintenance in flying ad hoc networks, a topology management technique based on connection estimate is presented [24]. To provide a reliable and efficient virtual backbone, a scheduling technique based on minimum CDS is suggested. For UAVs of the Urban Internet of Vehicles, stable clustering and MPR selection are dependent on node quality of service (QoS). The QoS function was created as a node stability metric using a Bayesian belief function that took environmental indicators into account [35]. An improved OLSR protocol based on changed willingness is proposed [36], and the OLSR protocol configurations are tuned to work with UANETs. In order to choose MPRs in OLSR based on the drone’s neighbourhood, energy, stability, and key utilisation, a stable path selection employing the whale and lion optimization method is designed [37]. For FANETs, a delay- and link-stability-based routing protocol has been created. According to the highest importance of the nodes, a red-black priority tree is built in their job. Nodes are designated for selection if their stability exceeds the threshold value [38]. The packets are routed based on the link stability with regard to the positions and speeds of the nodes. The Euclidean distance was used to calculate the location stability. The velocity stability is determined each time the UAV gets a HELLO packet. The components of this protocol are adaptive HELLO packet control and route repair [39]. A connected dominating set with MPR-based broadcasting strategy was put forth [40]. Multi-objective OLSR, an energy-conscious OLSR methodology, was put out by [41–44]. By taking into account the transmission power usage and residual energy within each node, they calculated a composite energy cost and used this composite energy index as the routing metric.

Destination-Sequenced Distance-Vector (DSDV) Routing named Improved Sequencing Heuristic-DSDV (ISH-DSDV) is proposed for the internet of flying vehicles [45]. The bellman-ford algorithm, which consists of routing updates, information broadcasting, and a stale approach, is presented by ISH-DSDV. A clustering technique that is energy-efficient is proposed to transmit data in sensor nodes during emergency disaster monitoring. When evaluating a node's suitability to serve as a cluster head, factors such as degree, transmission power, mobility, starting energy of each sensor node, trust value node, and distance from the base station to each sensor node are all taken into consideration. Additionally, the node energy level and communication link quality are taken into account when determining the optimum path to the destination following each of these processes, aggregation algorithms employing an XOR gate operation remove duplicate information from various nodes [46].

A routing method for the Internet of Everything (IoE), in which some IoE-objects in the UAV-enabled IoE (Ue-IoE) are given the task of route computation (from neighbour objects to destination). The route computation objects (RCO) are chosen based on various factors, such as mobility and energy remaining. When an RCO has to communicate with another item, they relay the routing information to its neighbours. To evenly spread the load, the work of RCO is rotated among all IoE-objects in Ue-IoE [47]. This prevents the routing tables of all Ue-IoE objects from being impacted by the topology's frequent changes. IoT is a key component in the Smart Transport Infrastructure (STI) era. They first thoroughly examine the vehicular network and STI before illuminating the blockchain and Federated Learning through actual-world applications. Then, from the perspectives of security and privacy, FL and blockchain applications in the Vehicular Ad Hoc Network (VANET) environment are thoroughly addressed [48–55].

We suggest a measure called SM that accounts for the three different cost metrics, Link Connectivity Index (as established in Section 4.1.2), Energy Weight (as defined in Section 4.1.3), and Degree Weight (as defined in Section 4.1.4), in order to determine the stability of a link. The predicted link expiration duration between the two nodes is calculated using the LCI measure. This statistic is used to identify the node that can provide a longer-lasting route and is more stable. Because nodes with higher energy must be chosen, the energy metric is employed to extend CDS lifetime. When nodes with more neighbours are chosen, CDS will be smaller in size.Therefore, our stability metric combines all three metrics to create the smallest CDS with the longest lifetime. Each node in the network computes its weights for energy and degree. It informs its one-hop neighbours of this knowledge. Following receipt of this data, each node determines the stability measure for each of its one-hop neighbours. The SM of a node u to its neighbor v can be defined as follows,

(1) SM(u,v)=α*LCI(u,v)+β*EW(v)+γ*DW(v)where α + β + γ = 1.

Our method may construct a CDS without any prior knowledge of the global network topology. Each node keeps a record of its one-hop and two-hop neighbours’ IDs. To support these updates, HELLO messages are sent on a regular basis. The following steps make up the proposed CDS selection process: Each node first chooses which group of one-hop neighbours it will use as its relay nodes in terms of stability metric. The relay set is then communicated to each node’s one-hop neighbours. Each node first sets its dominant flag to false. If x is the only node that can reach some of its neighbours, node v chooses one-hop neighbour x as its relay. If not, it selects the neighbour with the highest SM value as a one-hop neighbour. Up until all of the two-hop neighbours are covered, this process is repeated. The dominating flag is then set to true for each relay set node. A CDS is created for the network by all the dominant nodes. The selection process for CDS is shown in Algorithm 1.

This section explains the topology discovery and source routing in S-ELHR.

Fig. 1. illustrates how, as protocol nodes expand, so does the number of relay nodes. Nodes with less leftover energy are excluded by the weight-based willingness. The number of relay nodes is greatly decreased by the CDS construction with stability metric. Additionally, the suggested protocol S-ELHR chooses a reliable CDS that can offer a long-lasting routing path. The OLSR's MPR selection method does not account for difficulties with route stability. But in EE-OLSR energetic status is used MPR construction process. WILL DEFAULT and energetic status, respectively, are used in OLSR and EE-willingness-based OLSR's MPR selection. Comparing S-ELHR to EE-OLSR and OLSR, the figure demonstrates that S-ELHR has the smallest relay set size.

The performance of the networks is significantly influenced by the length of the shortest path linking the various sources and destinations. Longer paths cause the traffic flow's delay, jitter, and packet loss to increase. The average path lengths for the protocols are computed in order to assess the impact on the path lengths, and they are displayed in Fig. 2. S-ELHR performs better than OLSR and EE-OLSR because it chooses fewer CDS nodes in sparse networks. When the network is denser, the likelihood of shorter pathways is higher. In denser networks, the average path length for S-ELHR, OLSR, and EE-OLSR is almost the same. However, when compared to OLSR and EE-OLSR, the S-ELHR provides the shortest average path length.

The average number of topological messages sent by each node during the simulations is shown in Fig. 3a against network density. Since there are more relay nodes as the network size grows for the protocols, there are more topological messages. The stability of the CDS is taken care of by the connection index, degree, and energy measurements employed in S-ELHR. As a result, in OLSR, the path across these nodes has fewer link breakages than the path through MPR. The EE-OLSR protocol offers a more energy-rich path than OLSR since it considers the nodes' energy consumption as an MPR selection metric. EE-OLSR has more topology overhead than S-ELHR because of the bigger MPR set size. In contrast to OLSR and EE-OLSR, S-ELHR has minimal topological message overhead. The topology overhead of the protocols is seen to grow with changing speed in Fig. 3b. The increased topology overhead for the protocols is a result of the more topology change caused by faster nodes. When the node speed is more than 25 m/s, the MPR set frequently changes for both OLSR and EE-OLSR. More topological message forwarding results from this. S-ELHR has the least topological overhead among the protocols, but, as a result of the stability metric’s tendency to prevent frequent changes in the DS set.

Fig. 4 depicts the typical energy used for the planned work with various network sizes and node speeds. (a) and (b). The S-ELHR uses the least amount of energy when compared to the EE-OLSR and OLSR since it has minimal control overhead. Fig. 4b demonstrates how the energy consumption of the protocols rises as the speed does. Due to increased route breakage at speeds greater than 20 m/s, EE-OLSR and OLSR use more energy. S-ELHR uses the least amount of energy when compared to EE-OLSR and OLSR since it forwards messages across fewer, more stable nodes with minimal topology.