# Mutually orthogonal hamiltonian connected graphs

Tung-Yang Ho, Cheng-Kuan Lin, Jiann-Mean Tan, Lih-Hsing Hsu

Research output: Contribution to journalArticle

2 Scopus citations

### Abstract

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.
Original language English 1429-1431 3 Applied Mathematics Letters 22 9 https://doi.org/10.1016/j.aml.2009.01.058 Published - Sep 2009

### Keywords

• Hamiltonian
• Hamiltonian connected
• WK-recursive network