標題: | Mutually orthogonal hamiltonian connected graphs |
作者: | Ho, Tung-Yang Lin, Cheng-Kuan Tan, Jimmy J. M. Hsu, Lih-Hsing 資訊工程學系 Department of Computer Science |
關鍵字: | Hamiltonian;Hamiltonian connected;Interconnection networks |
公開日期: | 1-九月-2009 |
摘要: | in this work, we concentrate on those n-vertex graphs G with n >= 4 and (e) over bar <= n - 4. Let P(1) = < u(1), u(2),..., u(n)) and P(2) = (v(1), v(2),..., v(n)) be any two hamiltonian paths of G. We say that P(1) and P(2) are orthogonal if u(1) = v(1), u(n) = v(n), and u(q) not equal v(q) for q is an element of {2, n - 1}. We say that a set of hamiltonian paths {P(1), P(2),..., P(s)} of G are mutually orthogonal if any two distinct paths in the set are orthogonal. We will prove that there are at least two orthogonal hamiltonian paths of G between any two different vertices. Furthermore, we classify the cases such that there are exactly two orthogonal hamiltonian paths of G between any two different vertices. Aside from these special cases, there are at least three mutually orthogonal hamiltonian paths of G between any two different vertices. (C) 2009 Elsevier Ltd. All rights reserved. |
URI: | http://dx.doi.org/10.1016/j.aml.2009.01.058 http://hdl.handle.net/11536/6773 |
ISSN: | 0893-9659 |
DOI: | 10.1016/j.aml.2009.01.058 |
期刊: | APPLIED MATHEMATICS LETTERS |
Volume: | 22 |
Issue: | 9 |
起始頁: | 1429 |
結束頁: | 1431 |
顯示於類別: | 期刊論文 |