Strongly Menger connectedness of data center network and (n, k)-star graph

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10404823" target="_blank" >RIV/00216208:11320/19:10404823 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Ovkmw9lXbi" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Ovkmw9lXbi</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.tcs.2019.09.047" target="_blank" >10.1016/j.tcs.2019.09.047</a>

Result language
angličtina
Original language name
Strongly Menger connectedness of data center network and (n, k)-star graph
Original language description
A graph G = (V, E) is F-strongly Menger-vertex-connected (resp. Menger-edge-connected), if for a subgraph G - F of G with a conditional faulty vertex (resp. edge) set F subset of V (resp. F subset of E), each pair of vertices u and v are connected by min(deg(G-F) (u), deg(G-F )(v)} internally disjoint (resp. edge-disjoint) fault-free paths in G - F. Where deg(G-F) (u) and deg(G-F) (v) are the degrees of u and v in G - F, respectively. He et al. (2018) [7] introduced some sufficient conditions of F-strongly Menger (edge) connected for k-regular triangle-free graphs. In this paper, we consider the strongly Menger connectedness of two kinds of graphs with triangles: data center network D-k,D-n and (n, k)-star graph S-n.k. We prove D-k,D- n is (k - 1)-strongly Menger-vertex-connected, (n + k - 3)-strongly Mengeredge-connected of order 1, (2n + 2k - 8)-strongly Menger-edge-connected of order 2, and (3n + 3k - 15)-strongly Menger-edge-connected of order 3. Furthermore, we obtain S-n,S-k is (k - 2)-strongly Menger-vertex-connected, (n - 3)-strongly Menger-edge-connected of order 1, (2n - 8)-strongly Menger-edge-connected of order 2, and (3n - 15)-strongly Menger-edge-connected of order 3. (C) 2019 Elsevier B.V. All rights reserved.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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