Graph theory is becoming increasingly significant as it is applied to areas of mathematics and science & technology. It is being actively used in fields as varied as biochemistry, electrical engineering, computer science and operations research. Graph embedding is an important technique used in the study of computational capabilities of processor interconnection networks and task distribution. Embeddings of graphs from one class of graphs into another class have important applications in the field of computer science. In the design and implementation of parallel and distributed computing systems, one fundamental issue is the design of the interconnection network through which the computing elements can communicate efficiently. A measure of reliability and fault tolerance of the overall interconnection networks is given by the maximum number of nodes which can fail simultaneously without prohibiting other non-faulty nodes from communicating with others. In this work the authors discussed the embedding parameters such as dilation, congestion and wirelenth of certain interconnection networks. Further, they studied faulty interconnection networks.