In this paper, we propose a domain adaptation framework to address the device mismatch issue in acoustic scene classification leveraging upon neural label embedding (NLE) and relational teacher student learning (RTSL). Taking into account the structural relationships between acoustic scene classes, our proposed framework captures such relationships which are intrinsically device-independent. In the training stage, transferable knowledge is condensed in NLE from the source domain. Next in the adaptation stage, a novel RTSL strategy is adopted to learn adapted target models without using paired source-target data often required in conventional teacher student learning. The proposed framework is evaluated on the DCASE 2018 Task1b data set. Experimental results based on AlexNet-L deep classification models confirm the effectiveness of our proposed approach for mismatch situations. NLE-alone adaptation compares favourably with the conventional device adaptation and teacher student based adaptation techniques. NLE with RTSL further improves the classification accuracy.