The t/k-diagnosability and strong Menger connectivity on star graphs with conditional faults

Li, Pingshan; Xu, Min

doi:10.1016/j.tcs.2019.06.016

Cited by 16 publications

(1 citation statement)

References 18 publications

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“…The study on strong Menger vertex/edge connectedness attracts more and more researchers' attention. On one hand, the (conditional) strong Menger connectivity of many known networks were explored in literature, for example, star graph [9,12], hypercubes [13], folded hypercubes [21], hypercube-like networks [16], Cayley graphs generated by transposition trees [17], augmented cubes [2], bubble-sort star graph [1], balanced hypercubes [7] etc. On the other hand, the (conditional) strong Menger edge connectivity were investigated on hypercubes [14], folded hypercubes [3], hypercube-like networks [8], balanced hypercubes [7] etc.…”

Section: Introductionmentioning

confidence: 99%

Strong Menger connectedness of augmented $k$-ary $n$-cubes

Gu¹,

Chang²,

Hao³

2019

Preprint

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A connected graph G is called strongly Menger (edge) connected if for any two distinct vertices x, y of G, there are min{deg G (x), deg G (y)} vertex(edge)-disjoint paths between x and y. In this paper, we consider strong Menger (edge) connectedness of the augmented k-ary n-cube AQ n,k , which is a variant of k-ary n-cube Q k n . By exploring the topological proprieties of AQ n,k , we show that AQn,3 for n ≥ 4 (resp. AQ n,k for n ≥ 2 and k ≥ 4) is still strongly Menger connected even when there are 4n − 9 (resp. 4n − 8) faulty vertices and AQ n,k is still strongly Menger edge connected even when there are 4n − 4 faulty edges for n ≥ 2 and k ≥ 3. Moreover, under the restricted condition that each vertex has at least two fault-free edges, we show that AQ n,k is still strongly Menger edge connected even when there are 8n − 10 faulty edges for n ≥ 2 and k ≥ 3. These results are all optimal in the sense of the maximum number of tolerated vertex (resp. edge) faults.

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