Abstract
Consider a labeled and strongly oriented cycle (C-m) over right arrow and a set Gamma = {(C-n) over right arrow, (C-n) over left arrow}, where (C-n) over right arrow, (C-n) over left arrow are two labeled and strongly oriented cycles with the same underlying graph and opposite orientations. Let h : E ((C-m) over right arrow) -> Gamma be any function that sends to every edge of (C-m) over right arrow either (C-n) over right arrow or (C-n) over left arrow. The main goal of this paper is to study the underlying graph of the product (C-m) over right arrow circle times(h)Gamma, where the product is defined as follows:
V (C-m) over right arrow circle times(h)Gamma = V ((C-m) over right arrow) x V ((C-n) over right arrow)
((a,b), (c,d)) is an element of E ((C-m) over right arrow circle times(h)Gamma)
double left right arrow (a,c) is an element of E (C-m) over right arrow) boolean AND (b,d) is an element of h(a,b)
This product is of interest since it preserves many different types of labelings. For instance, edge-magic and super edge-magic labelings. In this paper, we also study the algorithmic complexity of determining when a diagraph (D) over right arrow can be factored using the product circle times(h) in terms of a given set of diagraphs Gamma. This is the main topic of the third section of the paper.