Bipanconnectivity and edge-fault-tolerant bipancyclicity of hypercubes

Edge-fault-tolerant bipanconnectivity of hypercubes

This paper shows that for any two distinct vertices u and vwith distance d in the hypercube Qn (n P 3) with at most 2n 5 faulty edges and each vertex incident with least two faultfree edges, there exist fault-free uv-paths of length ‘ in Qn for every ‘with dþ 4 6 ‘ 6 2 1 and ‘ d 0 ðmod2Þ. This result improves some known results on edge-fault bipanconnectivity of hypercubes. The proof is based o...

Edge-fault-tolerant edge-bipancyclicity of hypercubes

In this paper, we consider the problem embedding a cycle into the hypercube Qn with existence of faulty edges and show that for any edge subset F of Qn with |F | n− 1 every edge of Qn − F lies on a cycle of every even length from 6 to 2n inclusive provided n 4 and all edges in F are not incident with the same vertex. This result improves some known results.  2005 Published by Elsevier B.V.

Edge-pancyclicity and edge-bipancyclicity of faulty folded hypercubes

Let Fv and Fe be sets of faulty vertices and faulty edges, respectively, in the folded hypercube FQn so that |Fv| + |Fe| ≤ n − 2, for n ≥ 2. Choose any fault-free edge e. If n ≥ 3 then there is a fault-free cycle of length l in FQn containing e, for every even l ranging from 4 to 2 − 2|Fv |; if n ≥ 2 is even then there is a fault-free cycle of length l in FQn containing e, for every odd l rangi...

Edge-fault-tolerant properties of hypercubes and folded hypercubes

Edge-bipancyclicity of star graphs under edge-fault tolerant

The star graph Sn is one of the most famous interconnection networks. It has been shown by Li [T.-K. Li, Cycle embedding in star graphs with edge faults, Appl. Math. Comput. 167 (2005) 891–900] that Sn contains a cycle of length from 6 to n! when the number of fault edges in the graph does not exceed n 3. In this paper, we improve this result by showing that for any edge subset F of Sn with jFj...