R4-Graph: Integrating Sustainability into Discrete Mathematics Education Through Resilience-Oriented Graph Theory

The Education for Sustainable Development approach calls for mathematical tasks that illuminate the structure and changing behaviour of interdependent systems. This study develops R4-Graph, a four-phase sequence for sustainability-oriented discrete mathematics: Represent, Remove, Recover, and Redesign. The framework connects system modelling, vulnerability analysis, restoration strategies, and constrained network design through common graph representations and explicit mathematical tasks. Computational experiments covered 360 synthetic disturbance networks, 40 recovery networks, and 2112 link addition configurations across 12 spatial graphs; archived trajectories from the Catlins stream food web provided an environmental illustration. In preferential attachment networks, mean resilience was 0.5601 under random removal and 0.3776 under degree-targeted removal. Betweenness priority restoration yielded recovery resilience of 0.6817, compared with 0.6307 under random restoration. Spatial redesign exposed resilience–cost trade-offs, diminishing marginal improvements, and sensitivity to candidate edge selection. These results inform a four-stage teaching sequence with specified mathematical objectives, computational artefacts, and decision-making tasks for undergraduate discrete mathematics.