  Graph classification is a pivotal challenge in machine learning, especially
within the realm of graph-based data, given its importance in numerous
real-world applications such as social network analysis, recommendation
systems, and bioinformatics. Despite its significance, graph classification
faces several hurdles, including adapting to diverse prediction tasks, training
across multiple target domains, and handling small-sample prediction scenarios.
Current methods often tackle these challenges individually, leading to
fragmented solutions that lack a holistic approach to the overarching problem.
In this paper, we propose an algorithm aimed at addressing the aforementioned
challenges. By incorporating insights from various types of tasks, our method
aims to enhance adaptability, scalability, and generalizability in graph
classification. Motivated by the recognition that the underlying subgraph plays
a crucial role in GNN prediction, while the remainder is task-irrelevant, we
introduce the Core Knowledge Learning (\method{}) framework for graph
adaptation and scalability learning. \method{} comprises several key modules,
including the core subgraph knowledge submodule, graph domain adaptation
module, and few-shot learning module for downstream tasks. Each module is
tailored to tackle specific challenges in graph classification, such as domain
shift, label inconsistencies, and data scarcity. By learning the core subgraph
of the entire graph, we focus on the most pertinent features for task
relevance. Consequently, our method offers benefits such as improved model
performance, increased domain adaptability, and enhanced robustness to domain
variations. Experimental results demonstrate significant performance
enhancements achieved by our method compared to state-of-the-art approaches.
