The paths embedding of the arrangement graphs with prescribed vertices in given position

Yuan-Hsiang Teng (), Jimmy J. M. Tan (), Chey-Woei Tsay () and Lih-Hsing Hsu ()
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Yuan-Hsiang Teng: Hungkuang University
Jimmy J. M. Tan: National Chiao Tung University
Chey-Woei Tsay: Providence University
Lih-Hsing Hsu: Providence University

Journal of Combinatorial Optimization, 2012, vol. 24, issue 4, No 15, 627-646

Abstract: Abstract Let n and k be positive integers with n−k≥2. The arrangement graph A n,k is recognized as an attractive interconnection networks. Let x, y, and z be three different vertices of A n,k . Let l be any integer with $d_{A_{n,k}}(\mathbf{x},\mathbf{y}) \le l \le \frac{n!}{(n-k)!}-1-d_{A_{n,k}}(\mathbf{y},\mathbf{z})$ . We shall prove the following existance properties of Hamiltonian path: (1) for n−k≥3 or (n,k)=(3,1), there exists a Hamiltonian path R(x,y,z;l) from x to z such that d R(x,y,z;l)(x,y)=l; (2) for n−k=2 and n≥5, there exists a Hamiltonian path R(x,y,z;l) except for the case that x, y, and z are adjacent to each other.

Keywords: Arrangement graph; Panpositionable Hamiltonian; Panconnected; Interconnection network (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10878-011-9418-y

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