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GC
2007
Springer

Consistent Cycles in Graphs and Digraphs

13 years 3 months ago
Consistent Cycles in Graphs and Digraphs
Let Γ be a finite digraph and let G be a subgroup of the automorphism group of Γ. A directed cycle C of Γ is called G-consistent whenever there is an element of G whose restriction to C is the 1-step rotation of C. Consistent cycles in finite arc-transitive graphs were introduced by Conway in one of his public lectures. He observed that the number of G-orbits of G-consistent cycles of an arc-transitive group G is precisely one less than the valency of the graph. In this paper, we give a detailed proof of this result in a more general settings of arbitrary groups of automorphisms of graphs and digraphs.
Stefko Miklavic, Primoz Potocnik, Steve Wilson
Added 14 Dec 2010
Updated 14 Dec 2010
Type Journal
Year 2007
Where GC
Authors Stefko Miklavic, Primoz Potocnik, Steve Wilson
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