Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
471990 | Computers & Mathematics with Applications | 2009 | 7 Pages |
Abstract
It is proved that there exists a path Pl(x,y) of length ll if dAQn(x,y)≤l≤2n−1 between any two distinct vertices x and y of AQnAQn. Obviously, we expect that such a path Pl(x,y) can be further extended by including the vertices not in Pl(x,y) into a hamiltonian path from x to a fixed vertex z or a hamiltonian cycle. In this paper, we prove that there exists a hamiltonian path R(x,y,z;l) from x to z such that dR(x,y,z;l)(x,y)=l for any three distinct vertices x, y, and z of AQnAQn with n≥2n≥2 and for any dAQn(x,y)≤l≤2n−1−dAQn(y,z). Furthermore, there exists a hamiltonian cycle S(x,y;l) such that dS(x,y;l)(x,y)=l for any two distinct vertices x and y and for any dAQn(x,y)≤l≤2n−1.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science (General)
Authors
Chung-Meng Lee, Yuan-Hsiang Teng, Jimmy J.M. Tan, Lih-Hsing Hsu,