Connectivity plays an important role in measuring the fault tolerance of interconnection networks $G=(V,E)$. A faulty set $F⊆V$ is called a g-extra faulty set if every component of G−F has more than g nodes. A g-extra cut of G is a g-extra faulty set F such that G−F is disconnected. The minimum cardinality of g-extra cuts is said to be the g-extra connectivity of G. Diagnosability is an important metric for measuring the reliability of G. A new measure for fault diagnosis of G restrains that every fault-free component has at least $(g+1)$ fault-free nodes, which is called the g-extra diagnosability of G. As a favorable topology structure of interconnection networks, the n-dimensional bubble-sort star graph BS_n has many good properties. In this paper, we prove that 2-extra connectivity of BS_n is $6n−15$ for $n≥5$ and the 2-extra connectivity of BS₄ is 8; the 2-extra diagnosability of BS_n is $6n−13$ under the PMC model for $n≥5$ and the 2-extra diagnosability of BS_n is $6n−13$ under the MM^* model for $n≥6$.

Diagnosability is an important metric for measuring the reliability of multiprocessor systems. In 2012, Peng et al. proposed a new measure for fault tolerance of the system, which is called g-good-neighbour diagnosability that restrains every fault-free node containing at least g fault-free neighbours. As a favourable topology structure of interconnection networks, the Cayley graph $C{\mathrm{\Gamma }}_n$ generated by the transposition tree ${\mathrm{\Gamma }}_n$ has many good properties. In this paper, we give that the 1-good-neighbour diagnosability of $C{\mathrm{\Gamma }}_n$ under the PMC model and MM ${}^{\ast }$ model is $2n-3$ except the bubble-sort graph $B_4$ under MM ${}^{\ast }$ model, where $n\ge 4$, and the 1-good-neighbour diagnosability of $B_4$ under the MM ${}^{\ast }$ model is 4.

Accurately predicting stock prices is crucial for investment and risk management, but the non-stationarity of the financial market and the complex correlations among stocks pose challenges to traditional models (ARIMA, LSTM, XGBoost), resulting in difficulties in effectively capturing dynamic patterns and limited prediction accuracy. To this end, this paper proposes the Financial Spatio-Temporal Graph Attention Network (FSTGAT), with the following core innovations: temporal modelling through gated causal convolution to avoid future information leakage and capture long- and short-term fluctuations; enhanced spatial correlation learning by adopting the Dynamic Graph Attention Mechanism (GATv2) that incorporates industry information; designing the Multiple-Input-Multiple-Output (MIMO) architecture of industry grouping for the simultaneous learning of intra-group synergistic and inter-group influence; symmetrically fusing spatio-temporal modules to construct a hierarchical feature extraction framework. Experiments in the commercial banking and metals sectors of the New York Stock Exchange (NYSE) show that FSTGAT significantly outperforms the benchmark model, especially in high-volatility scenarios, where the prediction error is reduced by 45–69%, and can accurately capture price turning points. This study confirms the potential of graph neural networks to model the structure of financial interconnections, providing an effective tool for stock forecasting in non-stationary markets, and its forecasting accuracy and industry correlation capturing ability can support portfolio optimization, risk management improvement and supply chain decision guidance.