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In this paper, we present a new interconnection topology, called the[Formula: see text]-modified-bubble-sort graph, which is a generalization of the modified-bubble-sort graph. Additionally, we show many of its properties, such as its hierarchical structure, vertex transitivity, connectivity, edge-connectivity, super connectivity and super edge-connectivity. The [Formula: see text]-modified-bubble-sort graph presents more flexibility than the modified-bubble-sort graph in terms of its major design properties.

Diagnosability is an important factor in multiple-processor systems defined as the maximum number of faulty nodes that a system can recognize. In this paper, we propose a new form of diagnosability called non-inclusive diagnosability that requires all faulty sets to be non-inclusive. Furthermore, we study the non-inclusive diagnosability of hypercubes under the MM* model for [Formula: see text].

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