Embedding of 2 p -partite graphs into line graphs of arbitrary and binomial trees

Graph embedding is a key technique for mapping a guest graph onto a host graph. In architectural simulation, it is regarded as a powerful tool for executing parallel algorithms and simulating interconnection networks. In this work, we embed complete 2p-partite graphs into the line graph of an arbitrary tree. We also obtain the exact numeric value of the wirelength for embedding complete 2p-partite graphs into the line graph of a binomial tree. In addition, we compute the total number of 2-partition edge cuts in the line graph of a tree, providing structural insights for evaluating embedding efficiency.