In this paper, we address the problem of distillation-based class-incremental learning with a single head. A central theme of this task is to learn new classes that arrive in sequential phases over time while keeping the model’s capability of recognizing seen classes with only limited memory for preserving seen data samples. Many regularization strategies have been proposed to mitigate the phenomenon of catastrophic forgetting. To understand better the essence of these regularizations, we introduce a feature-graph preservation perspective. Insights into their merits and faults motivate our weighted-Euclidean regularization for old knowledge preservation. We further propose rectified cosine normalization and show how it can work with binary cross-entropy to increase class separation for effective learning of new classes. Experimental results on both CIFAR-100 and ImageNet datasets demonstrate that our method outperforms the state-of-the-art approaches in reducing classification error, easing catastrophic forgetting, and encouraging evenly balanced accuracy over different classes. Our project page is at : https://github.com/yhchen12101/FGP-ICL.