Finding Cut-Edges and the Minimum Spanning Tree via Semi-Tensor Product Approach

References

[1] Chung F. Graph theory in the information age. Notices of AMS, 2010, 57(6): 726–732.10.1090/cbms/107/01Search in Google Scholar

[2] Adolfo P M, Alkiviadis K, Victor M E, et al. Wikipedia information flow analysis reveals the scale-free architecture of the semantic space. PLoS One, 2011, 6(2): e17333.10.1371/journal.pone.0017333Search in Google Scholar PubMed PubMed Central

[3] Cheng D Z, Qi H S. Theory and application of matrix semi tensor product. Science Press, Beijing, 2007 (in Chinese).Search in Google Scholar

[4] Cheng D Z, Qi H S, Li Z Q. Analysis and control of Boolean networks: A semi-tensor product Approach. London: Springer, 2011.10.1007/978-0-85729-097-7Search in Google Scholar

[5] Cheng D Z, Qi H S. A linear representation of dynamics of Boolean networks. IEEE Transactions on Automatic Control, 2010, 55(10): 2251–2258.10.1109/TAC.2010.2043294Search in Google Scholar

[6] Li H T, Wang Y Z, Liu Z B. Existence and number of fixed points of Boolean transformations via the semi-tensor product method. Applied Mathematics Letters, 2012, 25(8): 1142–1147.10.1016/j.aml.2012.02.023Search in Google Scholar

[7] Dmitriy L, Michael M, Guy E. Observability of Boolean networks: A graph theoretic approach. Automatica, 2013, 49(8): 2351–2362.10.1016/j.automatica.2013.04.038Search in Google Scholar

[8] Ettore F, Maria E V. Observability, reconstructibility and state observers of Boolean control networks. IEEE Transactions on Automatic Control, 2013, 58(6): 1390–1401.10.1109/TAC.2012.2231592Search in Google Scholar

[9] Liu Y, Chen HW, Lu J Q, et al. Controiiability of probabilistic Boolean control networks based on transition probability matrices. Automatica, 2015, 52: 340–345.10.1016/j.automatica.2014.12.018Search in Google Scholar

[10] Liu Y, Lu J Q, Wu B. Some necessary and sufficient conditions for the out put controllability of temporal Boolean control networks. ESAIM Control Optimisation and Calculus of Variation, 2014, 20(1): 158–173.10.1051/cocv/2013059Search in Google Scholar

[11] Cheng D Z, Qi H S, Controllability and observability of Boolean control networks. Automatica, 2009, 45(7): 1659–1667.10.1016/j.automatica.2009.03.006Search in Google Scholar

[12] Zhong J, Lu J Q, Liu Y, et al. Synchronization in an array of outputcoupled Boolean networks with time delay. IEEE Transactions on Neural Networks and Learning Systems, 2014, 25(12): 2288–2294.10.1109/TNNLS.2014.2305722Search in Google Scholar PubMed

[13] Zhong J, Lu J Q, Huang T W, et al. Synchronization of master-slave Boolean networks with impulsive effects: Necessary and sufficient criteria. Neurocomputing, 2014, 143: 269–274.10.1016/j.neucom.2014.05.065Search in Google Scholar

[14] Lu J Q, Zhong J, Tang Y, et al. Synchronization in output-coupled temporal Boolean networks. Scientific Reports, 2014, 4: 6292.10.1038/srep06292Search in Google Scholar PubMed PubMed Central

[15] Li R, Chu T G. Complete synchronization of Boolean networks. IEEE Transactions on Neural Networks and Learning Systems, 2012, 23(5): 840–846.10.1109/TNNLS.2012.2190094Search in Google Scholar PubMed

[16] Li F F. Synchronization of coupled large-scale Boolean networks. Chaos, 2014, 24(1): 013115.10.1063/1.4863858Search in Google Scholar PubMed

[17] Cheng D Z. Disturbance decoupling of Boolean control networks. IEEE Transactions on Automatic Control, 2010, 20(3): 561–582.10.1109/TAC.2010.2050161Search in Google Scholar

[18] Cheng D Z, Li Z Q, Qi H S. Realization of Boolean control networks. Automatica, 2010, 46(1): 62–69.10.1016/j.automatica.2009.10.036Search in Google Scholar

[19] Laschov D, Margaliot M. A maximum principle for single-input boolean control networks. IEEE Transactions on Automatic Control, 2011, 56(4): 913–917.10.1109/TAC.2010.2101430Search in Google Scholar

[20] Li F F, Sun J T. Controllability of Boolean control networks with time delays in states. Automatica, 2011, 47(3): 603–607.10.1016/j.automatica.2011.01.040Search in Google Scholar

[21] Cheng D Z, Qi H S, He F G. Mapping and dynamic process on finite set use matrix semi tensor product method. Science Press, Beijing, 2015 (in Chinese).Search in Google Scholar

[22] Liu Y C, Zhang W. Boolean methodology. Shanghai Technology Literature Press, Shanghai, 1993 (in Chinese).Search in Google Scholar

[23] Reinhard D. Graph Theory, Graduate Texts in Mathematics. Fourth Edition. New York: Springer, 2010.Search in Google Scholar

[24] Wang Y Z, Zhang C G, Liu Z B. A matrix approach to graph maximum stable set and coloring problems with application to multi-agent systems. Automatica, 2012, 48(7): 1227–1236.10.1016/j.automatica.2012.03.024Search in Google Scholar