The Isoperimetric Number and The Bisection Width of Generalized Cylinders

A d–dimensional generalized cylinder is the Cartesian product of d graphs each of which is either a path graph or a cycle graph. In this paper, we use a simple embedding technique to find exact formulae for the edge–isoperimetric number and the bisection width of a cylinder in certain cases, e.g. when the size of the largest factor is even. operimetric number and the bisection width of d–dimensional tori (products of cycle graphs) and arrays (products of path graphs) are thus obtained as a byproduct under the same conditions. We also give description of an isoperimetric set as well as a bisection.