[Python] Langgraph: Getting ValueError: Found edge ending at unknown node `<function chatbot...

As part of experimenting Langgraph, i created below flow

def chatbot(state:State):
return {"messages":llm.invoke(state['messages'])}

def chat_history(state:State):
global chat_history
chat_history.append(state["messages"])
return state

def product_rec_prompt(state: State):
prompt_template = ChatPromptTemplate.from_messages(["prompt to get recommended product
from user query"])
formated_prompt = prompt_template.format_messages(topic=str(user_input))
response = llm.invoke(prompt_template.invoke(formated_prompt))
print(response)
return state


i added below flow and edge case

graph_builder.add_node("chatbot", chatbot)
graph_builder.add_edge(START, chatbot)
graph_builder.set_entry_point("chatbot")

graph_builder.add_node("chat_history",chat_history)

graph_builder.add_node("product_rec_prompt", product_rec_prompt)

# Define edge case to use chat history and recoomndation
graph_builder.add_edge("chat_history", "product_rec_prompt")
graph_builder.add_edge("product_rec_prompt", "chatbot")
graph_builder.add_edge("chatbot", END)
graph = graph_builder.compile()


but i am getting below error

raise ValueError(f"Found edge ending at unknown node `{target}`")
ValueError: Found edge ending at unknown node `<function chatbot at 0x0000029C45B4FF40>`


i hope the flow work as it is

Chatbot -> Start -> call chat_history -> call product_rec_prompt -> END


can you help with solution and right approach if applicable?

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