Distance formula and shortest paths for the (n,k)(n,k)-star graphs

The class of (n,k)(n,k)-star graphs is a generalization of the class of star graphs. Thus a distance formula for the first class implies one for the second. In this paper, we show that the converse is also true. Another important concept is the number of shortest paths between two vertices. This problem has been solved for the star graphs. We will solve the corresponding problem for the (n,k)(n,k)-star graphs.