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, 2 k < n . We also count the number of non-isomorphic signatures on P (2 n + 1, 1) of size two for all n ≥ 1 , and we conjecture that any signature of P (2 n + 1, 1) , up to switching, is of size at most n + 1 .