In this paper, we introduce the concept of vertex-edge locating Roman dominating functions in graphs. A vertex-edge locating Roman dominating \({(ve-LRD)}\) function of a graph \(G=(V,E)\) is a function \(f:V(G)\rightarrow\{0,1,2\}\) such that the following conditions are satisfied: (i) for every adjacent vertices \(u,v\) with \(f(u)=0\) or \(f(v)=0\), there exists a vertex \(w\) at distance \(1\) or \(2\) from \(u\) or \(v\) with \(f(w)=2\), (ii) for every edge \(uv\in E\), \(\max[f(u),f(v)]\neq 0\), and (iii) any pair of distinct vertices \(u,v\) with \(f(u)=f(v)=0\) does not have a common neighbour \(w\) with \(f(w)=2\). The weight of ve-LRD function is the sum of its function values over all the vertices. The vertex-edge locating Roman domination number of \(G\), denoted by \(\gamma_{veLR}(G)\), is the minimum weight of a {ve-LRD} function in \(G\). We proved that the vertex-edge locating Roman domination problem is NP-complete for bipartite graphs. Also, we present the upper and lower bounds of \({ve-LRD}\) function for trees. Lastly, we give the upper bounds of \({ve-LRD}\) function for some connected graphs.

Traditional personnel recruitment methods are often inefficient and struggle to find candidates who meet job requirements. In this paper, we first develop a comprehensive personnel management system for colleges and universities that streamlines the recruitment process and information management. Next, recruitment data from the system is analyzed using the fuzzy C-means algorithm to cluster applicant profiles and extract position-specific user characteristics. Finally, a joint embedded neural network is employed to match applicant profiles with job positions by optimizing an objective function. Experimental results demonstrate a high job matching rate (up to 98.1%), a significantly reduced recruitment cycle (from job posting to candidate onboarding in 25 days), and a system response time as low as 0.5 seconds. These findings highlight the effectiveness of big data technology in providing timely feedback, reducing recruitment costs and staff workload, and promoting the intelligent development of talent recruitment.

The rapid development of information technology makes intelligent decision support system play an increasingly important role in economic standardized management. The Intelligent Decision Support System (IDSS) constructed in this paper includes interaction layer, analysis layer and data layer. The system standardizes the management of enterprise economy through strategic forecasting and decision analysis, economic planning and control, and economic analysis. The study combines the fuzzy hierarchical analysis method (FAHP) and the fuzzy comprehensive evaluation method (FCE) to evaluate the standardized level of economic management of enterprise A. The evaluation score of the standardized level of enterprise A’s economic management is \(F=80.955\), which is greater than 80, and it belongs to the grade of “good”. It shows that the intelligent decision support system constructed based on this paper can effectively help standardize the management of enterprise economy.

In order to solve the multi-objective optimization problem of resource allocation in enterprise strategic management, the article firstly establishes a multi-objective resource allocation model for maximizing the benefits of enterprises in enterprise strategic management. Then, it optimizes and improves the initial population, convergence factor and dynamic weights of the gray wolf algorithm, increases the population diversity by using the population strategy of reverse learning, improves the convergence factor into a nonlinear factor, and finally changes the decision-making weights of the gray wolf leadership and applies the dynamic weights to improve the accuracy of the algorithm. Subsequently, the improved gray wolf algorithm is utilized for model decoupling. By applying this paper’s algorithm and the other two algorithms to solve the six algorithms 30*6, 60*6, 90*2, 90*4, 150*4 and 150*6 for 9 times, it is found that in the analysis of the 30*6 algorithm, the enterprise’s resource allocation reaches 5,000 when the time is 110 s. At the same time, this paper’s algorithm obtains a better non-dominated solution than the other two algorithms, which proves that this paper’s algorithm solves the multi-objective resource allocation problem of enterprise law industry is proved to be effective.

In food processing, foreign matter inevitably contaminates packaged food. To ensure food safety, ray-based detection is used; however, the original images suffer from aberrations and noise that degrade quality and hinder further processing. Thus, images are preprocessed to enhance quality by highlighting key features and suppressing irrelevant ones before abnormal pattern recognition. Following image segmentation, a BP neural network algorithm is applied for foreign object detection. In tests with contaminants such as metal wires, stones, and glass, the algorithm identified distinct abnormal fluctuations at gray levels of 132, 108, and 34, respectively, allowing it to reliably detect foreign objects. Although the practical detection rate reached 100%, occasional misjudgments suggest that further optimization is needed. Overall, this method introduces a novel approach to detecting foreign objects in food and offers promising new strategies for improving food safety monitoring.

An \( (n,r) \)-arc in \( \operatorname{PG}(2,q) \) is a set \( \mathcal{B} \) of points in \( \operatorname{PG}(2,q) \) such that each line in \( \operatorname{PG}(2,q) \) contains at most \( r \) elements of \( \mathcal{B} \) and such that there is at least one line containing exactly \( r \) elements of \( \mathcal{B} \). The value \( m_r(2,q) \) denotes the maximal number \( n \) of points in the projective geometry \( \operatorname{PG}(2,q) \) for which an \( (n,r) \)-arc exists. We show by systematically excluding possible automorphisms that putative \( (44,5) \)-arcs, \( (90,9) \)-arcs in \( \operatorname{PG}(2,11) \), and \( (39,4) \)-arcs in \( \operatorname{PG}(2,13) \)—in case of their existence—are rigid, i.e. they all would only admit the trivial automorphism group of order \( 1 \). In addition, putative \( (50,5) \)-arcs, \( (65,6) \)-arcs, \( (119,10) \)-arcs, \( (133,11) \)-arcs, and \( (146,12) \)-arcs in \( \operatorname{PG}(2,13) \) would be rigid or would admit a unique automorphism group (up to conjugation) of order \( 2 \).

Let \( S \) be a connected union of finitely many \( d \)-dimensional boxes in \( \mathbb{R}^d \) and let \( \mathcal{B} \) represent the family of boxes determined by facet hyperplanes for \( S \), with \( \mathcal{F} \) the associated family of faces (including members of \( \mathcal{B} \)). For set \( F \) in \( \mathcal{F} \), point \( x \) relatively interior to \( F \), and point \( y \) in \( S \), \( x \) sees \( y \) via staircase paths in \( S \) if and only if every point of \( F \) sees \( y \) via such paths. Thus the visibility set of \( x \) is a union of members of \( \mathcal{F} \), as is the staircase kernel of \( S \). A similar result holds for \( k \)-staircase paths in \( S \) and the \( k \)-staircase kernel of \( S \).

The minimum dominating set problem asks for a dominating set with minimum size. First, we determine some vertices contained in the minimum dominating set of a graph. By applying a particular scheme, we ensure that the resulting graph is 2-connected and the length of each formed induced cycle is 0 mod 3. We label every three vertices in the induced cycles of length 0 mod 3. Then there is a way of labeling in which the set of all labeled vertices is the minimum dominating set of the resulting graph, and is contained in the minimum dominating set of the original graph. We also consider the remaining vertices of the minimum dominating set of the original graph and determine all vertices contained in the minimum dominating set of a graph with maximum degree 3. The complexity of the minimum dominating set problem for cubic graphs was shown to be APX-complete in 2000 and this problem is solved by our arguments in polynomial time.

In this paper we study a new graph parameter, the stacking number. Defined in relation to the eternal domination game, we show that there are highly connected graphs for which it is beneficial to allow multiple guards to occupy a vertex, answering an open question of Finbow et al. In fact, we show that for any sequence \( (s_i) \), allowing \( s_j \) guards to occupy a vertex can save arbitrarily many guards in comparison to allowing fewer than this on a vertex. We also show that the stacking number is \( 1 \) for all trees.

The body language of dancers is vital for conveying emotion. In this study, Kinect is used to detect and track dancers’ movements, and we develop two models: a dance action recognition model based on skeleton data and a dance emotion recognition model using an Attention-ConvLSTM. The action recognition model achieves 88.34% accuracy—reaching its best performance after just 40 iterations—while the emotion recognition model reaches an accuracy of 98.95%. Our analysis shows that features such as eigenvalue speed, skeleton pair distance, and inclination effectively differentiate emotions, although certain emotions (e.g., Excited vs. Pleased and Relaxed vs. Sad) can be confused. Notably, the leg’s skeletal points significantly influence emotion expression. Ultimately, the study establishes a dance emotion expression mechanism through coordinated movement changes of the head, hands, legs, waist, and torso.