Vertex vulnerability parameters of Kronecker products of complete graphs

Mamut, Aygul; Vumar, Elkin

doi:10.1016/j.ipl.2007.12.002

Cited by 38 publications

(17 citation statements)

References 15 publications

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“…Regarding digraphs the ( , D, D , s)-problem has been considered for the general case in [33], for iterated line digraphs in [2,14,19,35], for Kautz digraphs in [17], for bipartite digraphs in [25,36], and for asymptotically optimal digraphs in [34]. See also [30] for products of graphs. Finally, [32] contains a comparative survey on vulnerability in graphs.…”

Section: Introduction and Some Previous Resultsmentioning

confidence: 99%

On large (Δ, D, D, 1)-graphs

2010

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Concern about fault tolerance in the design of interconnection networks has aroused interest in finding large graphs such that the subgraphs obtained by deleting any set of up to s vertices have small diameter. Clearly, 1 ≤ s ≤ − 1, where is the maximum degree of the graph. Graphs of maximum degree , diameter ≤ D and such that the graphs obtained by deletion of up to s vertices have diameter ≤ D are known as ( , D, D , s)graphs. This article considers the case s = 1 and D = D . In other words, it deals with the search for large graphs whose diameter does not increase after deleting one vertex. The article also contains an updated table of the largest known ( , D, D, 1)-graphs, in which most of the entries correspond to the constructions put forward in this article.

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Section: Introduction and Some Previous Resultsmentioning

confidence: 99%

On large (Δ, D, D, 1)-graphs

2010

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“…It has been shown that the Kronecker product is a good method to construct lager networks that can generate many good properties of the factor graphs (see [9]), and has received much research attention recently. Some properties and graphic parameters have been investigated [1,2,5,8,11]. The connectivity and diameter are two important parameters to measure reliability and efficiency of a network.…”

Section: Introductionmentioning

confidence: 99%

On the diameter of the Kronecker product graph

Hu¹,

Xu²

2013

Math. Sci. Lett.

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“…Vertex connectivity of K m × K n has been determined in [13], in [8] Guji and Vumar established the vertex connectivity of G × K n for a bipartite graph G. Moreover in [20] the authors determined the edge connectivity of G × K 2 . In [4], the general case was considered, and the authors obtained an upper bound and a lower bound on the edge connectivity of the direct products of two graphs.…”

Section: Introductionmentioning

confidence: 99%

“…(See[13].) Let m, n be integers with n m 2 and n 3, then κ(K m × K n ) = (m − 1)(n − 1).Theorem 1.2.…”

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confidence: 99%