Open Access
IEEE Access, volume 7, pages 17299-17311
Minimum Neighborhood of Alternating Group Graphs
3
Department of Computer Science, Montclair State University, Upper Montclair, NJ, USA
|
Publication type: Journal Article
Publication date: 2019-01-30
General Materials Science
General Engineering
General Computer Science
Abstract
The minimum neighborhood and combinatorial property are two important indicators of fault tolerance of a multiprocessor system. Given a graph G, θ
G
(q) is the minimum number of vertices adjacent to a set of q vertices of G (1 ≤ q ≤ |V(G)|). It is meant to determine θ
G
(q), the minimum neighborhood problem (MNP). In this paper, we obtain θ
AG0
(q) for an independent set with size q in an n-dimensional alternating group graph AGn, a well-known interconnection network for multiprocessor systems. We first propose some combinatorial properties of AGn. Then, we study the MNP for an independent set of two vertices and obtain that θ
AGn
(2) = 4n - 10. Next, we prove that θ
AGn
(3) = 6n -16. Finally, we propose that θ
AGn
(4) = 8n - 24.
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TY - JOUR
DO - 10.1109/access.2019.2896101
UR - https://doi.org/10.1109/access.2019.2896101
TI - Minimum Neighborhood of Alternating Group Graphs
T2 - IEEE Access
AU - Huang, Yanze
AU - Lin, Limei
AU - WANG, DAJIN
AU - Xu, Li
PY - 2019
DA - 2019/01/30
PB - Institute of Electrical and Electronics Engineers (IEEE)
SP - 17299-17311
VL - 7
SN - 2169-3536
ER -
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@article{2019_Huang,
author = {Yanze Huang and Limei Lin and DAJIN WANG and Li Xu},
title = {Minimum Neighborhood of Alternating Group Graphs},
journal = {IEEE Access},
year = {2019},
volume = {7},
publisher = {Institute of Electrical and Electronics Engineers (IEEE)},
month = {jan},
url = {https://doi.org/10.1109/access.2019.2896101},
pages = {17299--17311},
doi = {10.1109/access.2019.2896101}
}