On the edge-connectivity and restricted edge-connectivity of a product of graphs Original Research Article

The product graph image of two given graphs image and image was defined by Bermond et al. [Large graphs with given degree and diameter II, J. Combin. Theory Ser. B 36 (1984) 32–48]. For this kind of graphs we provide bounds for two connectivity parameters (image and image, edge-connectivity and restricted edge-connectivity, respectively), and state sufficient conditions to guarantee optimal values of these parameters. Moreover, we compare our results with other previous related ones for permutation graphs and cartesian product graphs, obtaining several extensions and improvements. In this regard, for any two connected graphs image, image of minimum degrees image, image, respectively, we show that image is lower bounded by both image and image, an improvement of what is known for the edge-connectivity of image.