Conditional fault-tolerant edge-bipancyclicity of hypercubes with faulty vertices and edges

A network is said to be conditionally faulty if its every vertex is incident to at least g fault-free neighbors, where g≥1. An n-dimensional folded hypercube FQn is a well-known variation of an n-dimensional hypercube Qn, which can be constructed from Qn by adding an edge to every pair of vertices with complementary addresses. In this paper, we define that a network is said to be g-conditionally faulty if its every vertex is incident to at least g fault-free neighbors, and let FFv (respectively, FFe) denote the set of faulty vertices (respectively, faulty edges) in FQn. Then, we consider for the cycles embedding properties in FQn−FFv−FFe with 4-conditionally faulty, as follows: (1) For n≥3, FQn−FFv−FFe contains a fault-free cycle of every even length from 4 to 2n−2|FFv|, where |FFn|+|FFe| ≤ 2n−5; (2) For even n≥4, FQn−FFv−FFe contains a fault-free cycle of every odd length from n+1 to 2n−2|FFv|−1, where |FFv|+|FFe| ≤ 2n−5.

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Conditional fault-tolerant edge-bipancyclicity of hypercubes with faulty vertices and edges

Cited by 2 publications

References 33 publications

Cycles embedding in folded hypercubes under the conditional fault model

Cycles embedding in folded hypercubes under the conditional fault model

Embedding Every Cycle in Conditionally Faulty Folded Hypercubes

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