Non-isomorphic signatures on some generalised Petersen graph

Abstract

In this paper we find the number of different signatures of P (3, 1), P (5, 1) and P (7, 1) up to switching isomorphism, where P (n, k) denotes the generalised Petersen graph, 2k < n. We also count the number of non-isomorphic signatures on P (2n + 1, 1) of size two for all n ≥ 1, and we conjecture that any signature of P (2n + 1, 1), up to switching, is of size at most n + 1.