Irregularity indices are usually used for quantitative characterization of the topological structures of non-regular graphs. In numerous problems and applications, especially in the fields of chemistry and material engineering, it is useful to be aware of the irregularity of a molecular structure. Furthermore, the evaluation of the irregularity of graphs is valuable not only for quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies but also for various physical and chemical properties, including entropy, enthalpy of vaporization, melting and boiling points, resistance, and toxicity. In this paper, we will restrict our attention to the computation and comparison of the irregularity measures of different classes of dendrimers. The four irregularity indices which we are going to investigate are $\sigma$ irregularity index, the irregularity index by Albertson, the variance of vertex degrees, and the total irregularity index.

Aiming at the problem of path planning for autonomous underwater vehicle (AUV) to cope with the influence of obstacles and eddies in complex marine environments, a path planning method based on an improved salp swarm algorithm (ISSA) is proposed. Firstly, the motion model of the AUV and eddy current model are constructed, including the relationship between position, velocity, attitude, and control inputs. Secondly, the improved SSA is proposed, which introduces the Levy flight strategy to enhance the algorithm’s optimization seeking ability and adds a nonlinear convergence factor to enhance the convergence ability of the algorithm. The stability and robustness of the improved algorithm are verified by test functions. Finally, the ISSA is applied to AUV path planning, which optimizes the AUV travel distance, improves the search efficiency and accuracy, and avoids the local optimum of the algorithm. The ISSA enhances the adaptive ability and robustness of the algorithm by introducing a dynamic adjustment strategy and feedback mechanism. Experimental verification is carried out using a simulated marine environment. The results show that the ISSA is better than the traditional algorithm in terms of path length as well as algorithm stability, and can effectively improve the navigation performance of AUV.

The time-sampling control strategy has communication discontinuities in the control of multiple AUVs (autonomous underwater vehicles). To overcome this problem, a distributed event-triggered communication mechanism is proposed to make each AUV communicate only when its own state is updated, which reduces the frequency of communication and improves the stability. This mechanism has better adaptability for formation control between heterogeneous AUV groups. At the same time, two consistency control algorithms based on event-triggered for homogeneous and heterogeneous AUV groups are studied, respectively. The known consistency algorithms are applied to the control of heterogeneous AUV groups for comparative analysis. The simulation results demonstrate that the number of communication among AUVs under the event-triggered control strategy can be significantly reduced. Therefore, the stability of the system is improved. Compared with the traditional consensus algorithm, the algorithm proposed in this paper has advantages in the control of heterogeneous AUV groups.

The deep-sea convergence zone (CZ) is a critical phenomenon for long-range underwater acoustic propagation. Accurate prediction of its distance, width, and gain is essential for enhancing sonar detection performance. However, conventional ray-tracing models, which assume vertically stratified sound speed profiles (SSPs), fail to account for horizontal sound speed gradients in the mixed layer, leading to significant prediction errors. To address this, we propose a novel ray-tracing model that incorporates horizontally inhomogeneous SSPs in the mixed layer. Our approach combines empirical orthogonal function (EOF) decomposition with the Del Grosso sound speed formula to construct a continuous 3D sound speed field. We further derive a modified ray equation including horizontal gradient terms and solve it using a fourth-order Runge–Kutta method. Simulation and experimental validation in the South China Sea demonstrate that our model reduces the prediction error for the first CZ distance by 2.26%, width by 2.66%, and gain deviation by 5.85% compared to the Bellhop model. These results confirm the effectiveness of our method in improving CZ parameter prediction accuracy.