The groups of the generalized Petersen graphs

Abstract

1.Introduction. For integersnandkwith 2 ≤ 2k <n, thegeneralized Petersen graph G(n, k)has been defined in (8) to have vertex-setand edge-setE(G(n, k))to consist of all edges of the formwhereiis an integer.All subscripts in this paper are to be read modulo n, where the particular value ofnwill be clear from the context. ThusG(n, k)is always a trivalent graph of order 2n, andG(5, 2) is the well known Petersen graph. (The subclass of these graphs withnandkrelatively prime was first considered by Coxeter ((2), p. 417ff.).)