End-to-end (E2E) Automatic Speech Recognition (ASR) has gained popularity in recent years, with most research focusing on designing novel neural network architectures, speech representations, and loss functions. However, the importance of topology in E2E ASR has been largely neglected. There are many aspects of topology to consider; in this paper, we focus on the relationship between topologies' minimum traversal time and output frame rate, the number of distinct states for each output unit, and the flexibility of alignments admitted. We ex- amine several different topologies on two datasets: WSJ and Librispeech. Our experiments reveal that different frame rates have varying optimal topologies and that the commonly used Connectionist Temporal Classification (CTC) topology is not always optimal. Our findings suggest that the choice of topology is an important consideration in the design of E2E ASR systems.