Cold-start item recommendation remains challenging as new items lack interaction signals beyond textual descriptions. Existing methods either fine-tune large language models (LLMs) on descriptions or map item content into collaborative spaces learned from user-warm item interactions. However, text-only prompts struggle to capture higher-order graph structures, while distributional differences between behavior and content embeddings weaken alignment based solely on predicted probabilities. To address these issues, we propose Graph Structure Serialization for Embedding Alignment (GraphSEA), an LLM-based framework inspired by the observation that graphs contain sequential structures similar to language and can be serialized as inputs for LLMs. GraphSEA first serializes interaction graphs into structured token sequences for an LLM to learn behavior embeddings that encode collaborative patterns, while the LLM separately generates content embeddings from item descriptions. An embedding alignment module then aligns behavior and content embeddings across multiple facets, including interaction probability, preference order, and item distinction. Extensive experiments demonstrate that GraphSEA improves recommendation performance across warm and cold recommendation tasks, while achieving higher efficiency than LLM-based methods.