Automorphisms of circulants that respect partitions
University of Calgary, Department of Mathematics & Statistics
In this paper, we begin by partitioning the edge (or arc) set of a circulant (di)graph according to which generator in the connection set leads to each edge. We then further reﬁne the partition by subdividing any part that corresponds to an element of order less than n, according to which of the cycles generated by that element the edge is in. It is known that if the (di)graph is connected and has no multiple edges, then any automorphism that respects the ﬁrst partition and ﬁxes the vertex corresponding to the group identity must be an automorphism of the group (this is in fact true in the more general context of Cayley graphs). We show that automorphisms that respect the second partition and ﬁx 0 must also respect the ﬁrst partition, and so are again precisely the group automorphisms of Zn.
Automorphism , Circulant graph , Caley graph
Morris, J. (2016). Automorphisms of circulants that respect partitions. Contributions to Discrete Mathematics, 11, 1-6