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On cycle permutation graphs. (English) Zbl 0559.05053
Cycle permutation graphs C(n,$$\alpha)$$ are those permutation graphs where the underlying graph is a cycle with n vertices of which $$\alpha$$ is a permutation. For some special types of cycle permutation graphs arising from certain kinds of permutations $$\alpha$$ the crossing numbers are determined. Among these permutations are transpositions and cyclic permutations. The second part of the paper studies the problem of which permutations yield isomorphic permutation graphs (for the same base graph). For the so-called k-twisted prism (where the permutation is a k- cycle) all permutations yielding isomorphic cycle permutation graphs are characterized.
Reviewer: W.Dörfler

##### MSC:
 05C99 Graph theory 05C10 Planar graphs; geometric and topological aspects of graph theory
##### Keywords:
Cycle permutation graphs; crossing numbers
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##### References:
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