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Neuromorphic hardware, designed to mimic the neural structure of the human brain, offers an energy-efficient platform for implementing machine-learning models in the form of Spiking Neural Networks (SNNs). Achieving efficient SNN execution on this hardware requires careful consideration of various objectives, such as optimizing utilization of individual neuromorphic cores and minimizing inter-core communication. Unlike previous approaches that overlooked the architecture of the neuromorphic core when clustering the SNN into smaller networks, our approach uses architecture-aware algorithms to ensure that the resulting clusters can be effectively mapped to the core. We base our approach on a crossbar architecture for each neuromorphic core. We start with a basic architecture where neurons can only be mapped to the columns of the crossbar. Our technique partitions the SNN into clusters of neurons and synapses, ensuring that each cluster fits within the crossbar's confines, and when multiple clusters are allocated to a single crossbar, we maximize resource utilization by efficiently reusing crossbar resources. We then expand this technique to accommodate an enhanced architecture that allows neurons to be mapped not only to the crossbar's columns but also to its rows, with the aim of further optimizing utilization. To evaluate the performance of these techniques, assuming a multi-core neuromorphic architecture, we assess factors such as the number of crossbars used and the average crossbar utilization. Our evaluation includes both synthetically generated SNNs and spiking versions of well-known machine-learning models: LeNet, AlexNet, DenseNet, and ResNet. We also investigate how the structure of the SNN impacts solution quality and discuss approaches to improve it.