Deques on a Torus

We provide an overview of graphical representations of stacks, queues, and deques. In the case of a cylinder book, corresponding to a deque, we give edge bounds and determine the deque number of the complete graph. We extend the deque in a natural way, forming a toroidal deque. Unlike the other three structures, the toroidal deque can process certain non-planar graphs, including \(K_7\) and the Cartesian product of two cycles.