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

A kind of conditional vertex connectivity of Cayley graphs generated by 2-trees

“…Such a structural result is useful in the study of other connectivity concepts. We note that the theme of fault tolerance with respect to certain properties is common, see [7,20,27,37] for some recent papers.…”

Edge-Bipancyclicity of Bubble-Sort Star Graphs

“…The edge-bipancyclicity and the bipancyclicity of different interconnection networks are widely studied. For example, see [10,11,13,14,15,20].…”

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

“…Study of the topological properties of an interconnection network is an important part of the study of any parallel or distributed system. Popular instances of interconnection networks include hypercubes [5], [26], star graphs [16] and k-ary n-cubes [2], [11], [21], [24]. The k-ary n-cube, denoted by Q k n , is the Cartesian product of cycles of the same length k. The hypercube is a k-ary n-cube with k ¼ 2.…”