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 $P(7,1)$ upto 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 $n \geq 1$, and we conjecture that any signature of $P(2n+1,1)$, upto switching, is of size at most $n+1$.