Path embeddings in faulty 3-ary n-cubes

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

“…Many works related to these embeddings in various interconnection networks have been studied previously [7], [8], [14], [15], [18], [20], [23], [27], [29], [32]. Embeddings of trees into networks play the most important role.…”

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

“…It is well known that Q k n is Hamiltonian [3] and Q k n with odd k is Hamilton-connected [11]. Recently, applications in parallel computing inspired the study of k-ary n-cubes with faulty edges, which lead to the investigation of Hamiltonian paths and cycles of Q k n avoiding a certain set of forbidden edges [1,15,17].…”

Edge-bipancyclicity of the k-ary n-cubes with faulty nodes and edges

“…Many researchers have investigated the pancyclicity and bipancyclicity of Q k n [5,6,10,[14][15][16][17]. Our primary motivation is the results of [14] where earlier results due to Hsieh et al [5] and to Wang et al [16] were extended and the situation as regards the pancyclicity and bipancyclicity of a fault-free Q k n was settled.…”