Abstract
In this paper, we define a kind of new product graphs with hexagonal inner faces, called semi-cartesian products, so that they directly link with hexagonal system, e.g., the semi-cartesian product of an even cycle and a path is a zigzag polyhex nanotube, a path and an even cycle is an armchair polyhex nanotube, two even cycles is a polyhex nanotorus and two paths is a polyhex lattice. Then we consider the distance in a semi-cartesian product and show two formulas to calculate the distance of two vertices and the sum of all pair of distances. Moreover we illustrate that the applying of the semi-cartesian products would be greatly simplifies the calculation of the distances in the carbon nanotubes and polyhex nanotorus by presenting some examples.
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