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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Theoretical Computer Science

ISSN

0304-3975

e-ISSN

—

Svazek periodika

799

Číslo periodika v rámci svazku

December

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

10

Strana od-do

94-103

Kód UT WoS článku

000504520500007

EID výsledku v databázi Scopus

2-s2.0-85073027943