A study of total relative displacements of permutations in paths and cycles

Kai Chung Cheng*, Hung-Lin Fu, Nam Po Chiang, Chien Kuo Tzeng

*Corresponding author for this work

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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 δΦ(G) is referred to as a near-automorphism of G and a permutation Φ which attains the maximum value of δΦ(G) is referred to as a chaotic mapping of G. In this paper, we study the maximum value of δΦ(G) among all permutations in paths and cycles.

Original languageEnglish
Pages (from-to)139-157
Number of pages19
JournalUtilitas Mathematica
Volume75
StatePublished - 1 Mar 2008

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    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.