Open Access

Shahab Abtahi

• Digital assessments in graph theory often resort to static images, offering neither interactivity nor variation between students. This thesis closes that gap by extending Moodle’s STACK plugin with JSXGraph visualisation and Maxima-based evaluation to deliver fully interactive, randomised exercises for Depth-First Search, Breadth-First Search, Dijkstra’s, and Kruskal’s algorithms. The system operates in five steps: (1) teachers specify controllable random-seed parameters; (2) Maxima constructs a tailored graph; (3) the graph is rendered live in the browser via JSXGraph; (4) students manipulate nodes and edges to express their solution; and (5) STACK evaluates the submission with algorithm-aware Maxima scripts, returning immediate feedback. A unifying input-capture layer means the same workflow supports all four algorithms, and a custom evaluation engine simulates each student’s logic to verify correctness. Pilottests with dozens of randomly generated instances confirm reliable grading and highlight the framework’s scalability. The work demonstrates how symbolic computation and client-side interactivity can be combined to raise both pedagogical value and assessment fidelity in digital learning environments.