Automorphisms of circulants that respect partitions

Morris, Joy

Automorphisms of circulants that respect partitions

dc.contributor.author	Morris, Joy
dc.date.accessioned	2018-07-10T17:10:45Z
dc.date.available	2018-07-10T17:10:45Z
dc.date.issued	2016
dc.description	Open access	en_US
dc.description.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.	en_US
dc.description.peer-review	Yes	en_US
dc.identifier.citation	Morris, J. (2016). Automorphisms of circulants that respect partitions. Contributions to Discrete Mathematics, 11, 1-6	en_US
dc.identifier.uri	https://hdl.handle.net/10133/5160
dc.language.iso	en_US	en_US
dc.publisher	University of Calgary, Department of Mathematics & Statistics	en_US
dc.publisher.department	Department of Mathematics and Computer Science	en_US
dc.publisher.faculty	Arts and Science	en_US
dc.publisher.institution	University of Lethbridge	en_US
dc.subject	Automorphism	en_US
dc.subject	Circulant graph	en_US
dc.subject	Caley graph	en_US
dc.subject.lcsh	Automorphisms
dc.subject.lcsh	Caley graphs
dc.subject.lcsh	Graph theory
dc.title	Automorphisms of circulants that respect partitions	en_US
dc.type	Article	en_US