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A vehicular ad hoc network is a dynamic and constantly changing topology that requires reliable clustering to prevent connection failure. A stable cluster head (CH) prevents packet delay (PD) and maintains high throughput in the network. This article presents a two-fold novel scheme for stable CH selection. In the first part of the proposed scheme, the vehicle network is considered a one-to-many connection network, which is near to a practical scenario. The cluster generation is handled using a newly proposed vehicular-hypergraph-based spectral clustering model. In the second part, the CH is selected considering the criteria for maintaining a stable connection with the maximum number of neighbours. The new rewarding/penalising relative speed and neighbourhood degree fulfil the condition. Eccentricity assesses that the vehicle should be at the centre of the cluster. Another metric with deep learning spectrum sensing is introduced for CH selection. Trust calculation is performed using deep learning-trained spectrum sensing as a model. The primary vehicle in noisy and noiseless environments is recognised using layers of long short-term memory. A high trust score is awarded to the vehicle which vacates the spectrum in the sensing of the primary vehicle. The stable CH selected by these metrics reduces the overhead that occurs due to the frequent shifting of the CH from one vehicle to another. This has been validated by the improved CH stability; increased cluster member (CM) lifetime and reduced rate of change of CH. The proposed scheme also demonstrates a considerable improvement in PD and throughput.