High renewable energy penetration continuously changes renewable generation, load, carbon prices, and regional exchange states, making fixed electricity-carbon relations insufficient for rolling dispatch. This paper proposes a GraphLLM-based low-carbon dispatch method that represents generation units, carbon quotas, regional grids, and their couplings in a time-varying attributed graph. A heterogeneous graph Transformer encodes typed relations, and a Q-Former maps graph representations and structured operating states to a Decoder-only large language model (LLM). The LLM generates node-state, edge-weight, and constraint updates, which are written back to the graph. A dual-timescale optimizer combines day-ahead adaptive particle swarm optimization (APSO) with hourly dynamic minimum-cost flow (dynamic MCF) to coordinate generation, carbon quota flows, and cross-regional trading. Across multiple datasets, the method reduces total cost and carbon emissions by about 7.8% and 10.5%, respectively, while lowering the constraint violation rate to 1.7%.