Strongly Menger-edge-connectedness and strongly Menger-vertex-connectedness of regular networks

There are a number of papers with results for r=2 for several popular classes of interconnection network. In this paper, we develop a unified approach by considering various sufficient conditions of a regular graph to be F-strongly Menger-edge-connected of order r and the corresponding vertex version. As corollaries, several results on fundamental classes of interconnection networks are presented including new results as well as strengthening of existing results such as the one given by Qiao and Yang (2017) [20].