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Corrigendum on Wiener index, Zagreb Indices and Harary index of Eulerian graphs
In the original article ``Wiener index of Eulerian graphs'' [Discrete Applied
Mathematics Volume 162, 10 January 2014, Pages 247-250], the authors state that
the Wiener index (total distance) of an Eulerian graph is maximized by the
cycle. We explain that the initial proof contains a flaw and note that it is a
corollary of a result by Plesn\'ik, since an Eulerian graph is
-edge-connected. The same incorrect proof is used in two referencing papers,
``Zagreb Indices and Multiplicative Zagreb Indices of Eulerian Graphs'' [Bull.
Malays. Math. Sci. Soc. (2019) 42:67-78] and ``Harary index of Eulerian
graphs'' [J. Math. Chem., 59(5):1378-1394, 2021]. We give proofs of the main
results of those papers and the -edge-connected analogues.Comment: 5 Pages, 1 Figure Corrigendum of 3 papers, whose titles are combine
Recent advances on recursive filtering and sliding mode design for networked nonlinear stochastic systems: A survey
Copyright © 2013 Jun Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Some recent advances on the recursive filtering and sliding mode design problems for nonlinear stochastic systems with network-induced phenomena are surveyed. The network-induced phenomena under consideration mainly include missing measurements, fading measurements, signal quantization, probabilistic sensor delays, sensor saturations, randomly occurring nonlinearities, and randomly occurring uncertainties. With respect to these network-induced phenomena, the developments on filtering and sliding mode design problems are systematically reviewed. In particular, concerning the network-induced phenomena, some recent results on the recursive filtering for time-varying nonlinear stochastic systems and sliding mode design for time-invariant nonlinear stochastic systems are given, respectively. Finally, conclusions are proposed and some potential future research works are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grant nos. 61134009, 61329301, 61333012, 61374127 and 11301118, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant no. GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany
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