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Panpositionable hamiltonicity of the alternating group graphs
Author(s) -
Teng YuanHsiang,
Tan Jimmy J.M.,
Hsu LihHsing
Publication year - 2007
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.20184
Subject(s) - combinatorics , mathematics , hamiltonian path , graph , cayley graph , hamiltonian (control theory) , discrete mathematics , mathematical optimization
The alternating group graph A G n is an interconnection network topology based on the Cayley graph of the alternating group. There are some interesting results concerning the hamiltonicity and the fault tolerant hamiltonicity of the alternating group graphs. In this article, we propose a new concept called panpositionable hamiltonicity. A hamiltonian graph G is panpositionable if for any two different vertices x and y of G and for any integer l satisfying d ( x , y ) ≤ l ≤ ∣ V ( G )∣− d ( x , y ), there exists a hamiltonian cycle C of G such that the relative distance between x , y on C is l . We show that A G n is panpositionable hamiltonian if n ≥ 3. © 2007 Wiley Periodicals, Inc. NETWORKS, Vol. 50(2), 146–156 2007