TY - JOUR

T1 - h-restricted connectivity of locally twisted cubes

AU - Wei, Chia Chen

AU - Hsieh, Sun Yuan

N1 - Funding Information:
This work was supported in part by the National Science Council under grant 103-2221-E-006-135-MY3 .
Funding Information:
This research was supported in part by (received funding from) the Headquarters of University Advancement at National Cheng Kung University, which is sponsored by the Ministry of Education, Taiwan, ROC.
Funding Information:
This research was supported in part by (received funding from) the Headquarters of University Advancement at National Cheng Kung University , which is sponsored by the Ministry of Education, Taiwan, ROC .
Publisher Copyright:
© 2016 Elsevier B.V.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2017/1/30

Y1 - 2017/1/30

N2 - Given a graph G and a non-negative integer h, the h-restricted connectivity of G, denoted by κh(G), is defined as the minimum size of a set X of nodes in G (X⊂V(G)) such that G−X is disconnected, and the degree of each component in G−X is at least h. The h-restricted connectivity measure is a generalization of the traditional connectivity measure, and it improves the connectivity measurement accuracy. Moreover, studies have revealed that if a network possesses a restricted connectivity property, it is more reliable and demonstrates a lower node failure rate compared with other networks. The n-dimensional locally twisted cube LTQn, which is a well-known interconnection network for parallel computing, is a variant of the hypercube Qn. Most studies have examined the h-restricted connectivity of networks under the conditions of h=1 or h=2. This paper examines a generalized h-restricted connectivity measure for n-dimensional locally twisted cube and reveals that κh(LTQn)=2h(n−h) for 0≤h≤n−2.

AB - Given a graph G and a non-negative integer h, the h-restricted connectivity of G, denoted by κh(G), is defined as the minimum size of a set X of nodes in G (X⊂V(G)) such that G−X is disconnected, and the degree of each component in G−X is at least h. The h-restricted connectivity measure is a generalization of the traditional connectivity measure, and it improves the connectivity measurement accuracy. Moreover, studies have revealed that if a network possesses a restricted connectivity property, it is more reliable and demonstrates a lower node failure rate compared with other networks. The n-dimensional locally twisted cube LTQn, which is a well-known interconnection network for parallel computing, is a variant of the hypercube Qn. Most studies have examined the h-restricted connectivity of networks under the conditions of h=1 or h=2. This paper examines a generalized h-restricted connectivity measure for n-dimensional locally twisted cube and reveals that κh(LTQn)=2h(n−h) for 0≤h≤n−2.

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U2 - 10.1016/j.dam.2016.08.012

DO - 10.1016/j.dam.2016.08.012

M3 - Article

AN - SCOPUS:84994464076

VL - 217

SP - 330

EP - 339

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -