### Abstract

Let G = (V, E) be a connected graph and let Φ be a permutation of V. The total relative displacement of the permutation Φ in G is {equation presented} where d(x, y) means the distance between x and y in G, i.e., the length of a shortest path between x and y. A permutation Φ which attains the minimum value of non-zero value of δ_{Φ}(G) is referred to as a near-automorphism of G and a permutation Φ which attains the maximum value of δ_{Φ}(G) is referred to as a chaotic mapping of G. In this paper, we study the maximum value of δ_{Φ}(G) among all permutations in paths and cycles.

Original language | English |
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Pages (from-to) | 139-157 |

Number of pages | 19 |

Journal | Utilitas Mathematica |

Volume | 75 |

State | Published - 1 Mar 2008 |

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## Cite this

Cheng, K. C., Fu, H-L., Chiang, N. P., & Tzeng, C. K. (2008). A study of total relative displacements of permutations in paths and cycles.

*Utilitas Mathematica*,*75*, 139-157.