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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.17542 |
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Table of Contents:
- We give an extension of the $G$ method, with results, the extension and results being partly suggested by the finite Markov chains and specially by the finite-time consensus problem for the DeGroot model and that for the DeGroot model on distributed systems. For the (homogeneous and nonhomogeneous) DeGroot model, using the $G$ method, a result for reaching a partial or total consensus in a finite time is given. Further, we consider a special submodel/case of the DeGroot model, with examples and comments -- a subset/subgroup property is discovered. For the DeGroot model on distributed systems, using the $G$ method too, we have a result for reaching a partial or total (distributed) consensus in a finite time similar to that for the DeGroot model for reaching a partial or total consensus in a finite time. Then we show that for any connected graph having $2^{m}$ vertices, $m\geq 1,$ and a spanning subgraph isomorphic to the $m$-cube graph, distributed averaging is performed in $m$ steps -- this result can be extended -- research work -- for any graph with $n_{1}n_{2}...n_{t}$ vertices under certain conditions, where $t,$ $n_{1},n_{2},...,n_{t}\geq 2,$ and, in this case, distributed averaging is performed in $t$ steps.