On optimal orientation of cycle vertex multiplications Original Research Article

For a bridgeless connected graph G, let image be the family of its strong orientations; and for any image, we denote by image its diameter. The orientation number image of G is defined by image. For a connected graph G of order n and for any sequence of n positive integers image, let image denote the graph with vertex set image and edge set image such that image, where imageʹs are pairwise disjoint sets with image, image, and for any two distinct vertices x, y in image, image if and only if image and image for some image with image such that image. We call the graph image a G vertex multiplication. In this paper, we determine the orientation numbers of various cycle vertex multiplications.