## 3 Proposed Method
Put simply, if the cluster head fails to meet the specified constraints, it should augment its transmission range (\(\beta_{\chi_{i}}\)) by adding \(\Delta\) to it (\(\beta_{\chi_{i}}=\beta_{\chi_{i}}+\Delta\)). In the third stage, after clustering, a new routing method is introduced for improved results between the source (\(S\)) and destination (\(D\)). This routing method focuses on inter-cluster communication, allowing each cluster to have limited connections with other clusters. This enables optimal selection of subsequent transfer and forwarding nodes towards the destination. Limiting the common members serves two purposes. Firstly, it ensures optimal clustering and unique members for each cluster. Secondly, the common members are responsible for routing as they can carry packets between clusters. Figure 2 illustrates a cluster configuration with common members, which means that each cluster communicates with other clusters (\(2\leq~{}OD\leq 5\)) through common members. For example, envision a situation where the source node \(V_{1}\) inside cluster \(C_{1}\) sends a packet intended for \(V_{10}\) to its cluster head \(\chi_{1}\). Afterward, \(\chi_{1}\) relays the packet to a common member, \(\aleph_{1}\), which serves as the intermediary node shared between clusters \(C_{1}\) and \(C_{2}\). As \(\aleph_{1}\) is a shared member between the two clusters, it is able to communicate with the cluster head of the other cluster \(\chi_{2}\) and transfer packets to \(\chi_{2}\). If \(\chi_{2}\) finds the destination node in its list, it dispatches the packet to \(V_{10}\). Otherwise, the packet is routed to the shared node \(\aleph_{2}\) in other clusters until it reaches the intended destination. This packet routing process can be depicted as follows:  
\[V_{1}\rightarrow\chi_{1}\rightarrow\aleph_{1} \begin{cases}V_{10}~{}~{}~{}if~{} V_{10}\in\chi_{2}\\ \chi_{2}\rightarrow\aleph_{2}\rightarrow\aleph_{3}\to V_{10},...\end{cases}  \tag{9}\]This method follows a reliable routing to the destination of the packet. In the final stage, after a time interval, clustering is conducted again and phases one, two, and three are repeated. Due to the high mobility of nodes in these networks, any node can leave the cluster and new nodes can join the cluster. According to the four phases mentioned above, we present the proposed Algorithm 1. As shown in the algorithm, when a node \(V_{2}\) wants to send a message to a vehicle at a great distance (\(V_{12}\)), vehicles receive information from GPS. The distance between each vehicle is then calculated using the Euclidean distance (from lines 1 to 5). \(\chi_{i}\) with the highest encounter rate and maximum remaining energy is selected for a group of vehicles (lines 6, 7, and 8). As long as conditions (\(M_{i}<5\) OR \(OD<2\)) AND \((\beta_{\chi_{i}}\leq R\ AND\ \chi_{i}\
eq\aleph_{q})\) are not fulfilled, the cluster head maintains the capability to enhance its transmission range by the value of \(\Delta\) (lines 9 and 10). The routing phase starts, and the source node \(V_{2}\) into cluster sends a message to its cluster head \(\chi_{1}\) (line 12). The \(\chi_{1}\) looks into the list of members, and as explained above, each cluster head has its own table (list) of members. If the destination node is not on the \(\chi_{i}\)'s list of members, the packet is sent to the \(\aleph_{q}\) (it can be seen in lines 13 to 17). The next step is for the \(\aleph_{q}\) to send the packets to the neighboring cluster head \(\chi_{2}\) that it is a member of, and so on until the packet reaches its destination \(V_{12}\), these steps will be repeated (line 20). Furthermore, the updating interval is independent of the contact duration, emphasizing that the number of encounters is the determining factor in our algorithm.