On the number of geodesics of Petersen graph GP(n,2)

For each n and k(n>2k), the generalized Petersen graph GP (n, k) is a trivalent graph with vertex set {ui,vi|0≤i≤n−1} and edge set {uiui+1,uivi,vivi+k|0≤i≤n−1, subscripts reduced modulo n}. There are three kinds of edges - outer edges, spokes and inner edges. Outer vertices generate an n-cycle called outer cycle and the inner vertices generate one or more cycles called inner cycles. In this paper, we consider the number of shortest paths or geodesics between two vertices of GP (n, 2).