On Consensus Index of Triplex Star-like Networks: A Graph Spectra Approach
In this article, the consensus-related performances of the triplex multi-agent systems with star-related structures, which can be measured by the algebraic connectivity and network coherence, have been studied by the characterization of Laplacian spectra. Some notions of graph operations are introdu...
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doaj-cbb35940c8c043c1b7c021e49202fc242021-07-23T14:09:25ZengMDPI AGSymmetry2073-89942021-07-01131248124810.3390/sym13071248On Consensus Index of Triplex Star-like Networks: A Graph Spectra ApproachDa Huang0Jian Zhu1Zhiyong Yu2Haijun Jiang3Department of Mathematics and Physics, Xinjiang Institute of Engineering, Urumqi 830023, ChinaDepartment of Mathematics and Physics, Xinjiang Institute of Engineering, Urumqi 830023, ChinaCollege of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, ChinaCollege of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, ChinaIn this article, the consensus-related performances of the triplex multi-agent systems with star-related structures, which can be measured by the algebraic connectivity and network coherence, have been studied by the characterization of Laplacian spectra. Some notions of graph operations are introduced to construct several triplex networks with star substructures. The methods of graph spectra are applied to derive the network coherence, and some asymptotic behaviors of the indices have been derived. It is found that the operations of adhering star topologies will make the first-order coherence increase a constant value under the triplex structures as parameters tend to infinity, and the second-order coherence have some equality relations as the node related parameters tend to infinity. Finally, the consensus related indices of the triplex systems with the same number of nodes but non-isomorphic graph structures have been compared and simulated to verify the results.https://www.mdpi.com/2073-8994/13/7/1248consensuscoherenceCartesian productconvergence speedrobustnessLaplacian spectrum |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Da Huang Jian Zhu Zhiyong Yu Haijun Jiang |
spellingShingle |
Da Huang Jian Zhu Zhiyong Yu Haijun Jiang On Consensus Index of Triplex Star-like Networks: A Graph Spectra Approach Symmetry consensus coherence Cartesian product convergence speed robustness Laplacian spectrum |
author_facet |
Da Huang Jian Zhu Zhiyong Yu Haijun Jiang |
author_sort |
Da Huang |
title |
On Consensus Index of Triplex Star-like Networks: A Graph Spectra Approach |
title_short |
On Consensus Index of Triplex Star-like Networks: A Graph Spectra Approach |
title_full |
On Consensus Index of Triplex Star-like Networks: A Graph Spectra Approach |
title_fullStr |
On Consensus Index of Triplex Star-like Networks: A Graph Spectra Approach |
title_full_unstemmed |
On Consensus Index of Triplex Star-like Networks: A Graph Spectra Approach |
title_sort |
on consensus index of triplex star-like networks: a graph spectra approach |
publisher |
MDPI AG |
series |
Symmetry |
issn |
2073-8994 |
publishDate |
2021-07-01 |
description |
In this article, the consensus-related performances of the triplex multi-agent systems with star-related structures, which can be measured by the algebraic connectivity and network coherence, have been studied by the characterization of Laplacian spectra. Some notions of graph operations are introduced to construct several triplex networks with star substructures. The methods of graph spectra are applied to derive the network coherence, and some asymptotic behaviors of the indices have been derived. It is found that the operations of adhering star topologies will make the first-order coherence increase a constant value under the triplex structures as parameters tend to infinity, and the second-order coherence have some equality relations as the node related parameters tend to infinity. Finally, the consensus related indices of the triplex systems with the same number of nodes but non-isomorphic graph structures have been compared and simulated to verify the results. |
topic |
consensus coherence Cartesian product convergence speed robustness Laplacian spectrum |
url |
https://www.mdpi.com/2073-8994/13/7/1248 |
work_keys_str_mv |
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1721285670236848128 |