Automorphisms of circulants that respect partitions
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Date
2016
Authors
Morris, Joy
Journal Title
Journal ISSN
Volume Title
Publisher
University of Calgary, Department of Mathematics & Statistics
Abstract
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.
Description
Open access
Keywords
Automorphism , Circulant graph , Caley graph
Citation
Morris, J. (2016). Automorphisms of circulants that respect partitions. Contributions to Discrete Mathematics, 11, 1-6