  To address the issue of insufficient knowledge and the tendency to generate
hallucination in Large Language Models (LLMs), numerous studies have endeavored
to integrate LLMs with Knowledge Graphs (KGs). However, all these methods are
evaluated on conventional Knowledge Graph Question Answering (KGQA) with
complete KGs, where the factual triples involved in each question are entirely
covered by the given KG. In this situation, LLM mainly acts as an agent to find
answer entities by exploring the KG, rather than effectively integrating
internal and external knowledge sources. However, in real-world scenarios, KGs
are often incomplete to cover all the knowledge required to answer questions.
To simulate real-world scenarios and evaluate the ability of LLMs to integrate
internal and external knowledge, in this paper, we propose leveraging LLMs for
QA under Incomplete Knowledge Graph (IKGQA), where the given KG doesn't include
all the factual triples involved in each question. To handle IKGQA, we propose
a training-free method called Generate-on-Graph (GoG) that can generate new
factual triples while exploring on KGs. Specifically, we propose a
selecting-generating-answering framework, which not only treat the LLM as an
agent to explore on KGs, but also treat it as a KG to generate new facts based
on the explored subgraph and its inherent knowledge. Experimental results on
two datasets demonstrate that our GoG can solve IKGQA to a certain extent,
while almost all previous methods cannot perform well on IKGQA.
