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.

Keywords

• signed graph, generalised petersen graph, balance, switching, switching isomorphism