Fault-Free Hamiltonian Cycles Passing through Prescribed Edges in <formula formulatype="inline"><tex Notation="TeX">$k$</tex> <mathgraphic graphicformat="GIF" fileref="zhang-ieq1-2311794.gif"/></formula>-Ary <formula formulatype="inline"><tex Notation="TeX"> $n$</tex><mathgraphic graphicformat="GIF" fileref="zhang-ieq2-2311794.gif"/></formula>-Cubes with Faulty Edges

Abstract

The k-ary n-cube Q k n is one of the most attractive interconnection networks for parallel and distributed systems.

A note on Hamiltonian paths and cycles with prescribed edges in the 3-ary n-cube

“…What is perhaps worse, the main result in [5] has been used to obtain further results by some other researchers (see for example [2,6]). In this note, we will give a counterexample and provide a correct proof.…”