Minimum algebraic connectivity of graphs whose complements are bicyclic with two cycles

References

• A. Z. Abdian, S. Pouyandeh, B. Askari, Which multicone graphs are determined by their signless Laplacian spectrum? (The proof of a conjecture), Journal of Discrete Mathematical Sciences and Cryptography, 22 1(2019), 91-99. doi: 10.1080/09720529.2019.1578082
   Web of Science ®Google Scholar
• D. Cvetković, M. Doob and H. Sachs, Spectra of Graphs, 3rd ed., Johann Ambrosius Barth, Heidelberg, 1995.
   Google Scholar
• D. Cvetković, P. Rowlinson and S. Simić, Eigenspaces of graphs, Cambridge Univ. Press, Cambridge, 1997.
   Google Scholar
• G. Jiang, G. Yu and J. Cao, The least algebraic connectivity of graphs, Discrete Dynamics in Nature and Society, vol. 2015, Article ID 756960.
   Web of Science ®Google Scholar
• I. Gutman, Some properties of Laplacian eigenvetors, Bulletin CXX VII Acad. Serbe 2003, Classes Sci. Math. naturelles Sciences math, No 28.
   Google Scholar
• M. Javaid, Masood Ur Rehman, On the second minimum algebraic connectivity of the graphs whose complements are trees, AKCE International Journal of Graphs and Combinatorics, 14(3), (2017): 233-241. doi: 10.1016/j.akcej.2017.03.005
   Web of Science ®Google Scholar
• M. Javaid, Minimizing graph of the connected graphs whose complements are bicyclic with two cycles, Turk. J. Math., 41(2017): 1433–1445. doi: 10.3906/mat-1608-6
   Web of Science ®Google Scholar
• M. Javaid, Characterization of the minimizing graph of the connected graphs whose complements are bicyclic, Mathematics, 5(2017): 1-12. doi: 10.3390/math5010018
   Web of Science ®Google Scholar
• M. Fiedler, Algebraic connectivity of graphs, Czechoslovak Mathematical Journal, 23(1973): 298-305.
   Web of Science ®Google Scholar
• Qun Liu, The Laplacian spectrum of corona of two graphs, Kragujevac Journal of Mathematics 38, 1(2014): 163-170. doi: 10.5937/KgJMath1401163L
   Google Scholar
• R. Grone, R. Merris, The Laplacian spectrum of a graph II, SIAM J. Discr. Math., 7(1994): 221-229. doi: 10.1137/S0895480191222653
   Web of Science ®Google Scholar
• R. Grone, R. Merris and V. S. Sunder, The Laplacian spectrum of a graph, SIAM J. Matrix Anal. Appl., 11(1990): 218-238. doi: 10.1137/0611016
   Web of Science ®Google Scholar
• R. Olfati-Saber, J. A. Fax, and R. M. Murray, Consensus and cooperation in networked multy-agent systems, Proceedings of the IEEE, vol. 95(2007): 215-233. doi: 10.1109/JPROC.2006.887293
   Web of Science ®Google Scholar
• Y. Tang, H. Gao, and J. Kurths, Distributed robust synchronization of dynamical networks with stochastic coupling, IEEE Transactions on circuits and Systems I: Regular Papers, 61(2014): 1508-1519. doi: 10.1109/TCSI.2013.2285699
   Web of Science ®Google Scholar
• Y. Tang, Z. Wang, H. Gao, S. Swift and J. Kurths, A constrained evolutionary computation method for detecting controlling regions of cortical networks, IEEE/ACM Transations on Computational Biology and Bioinformatics, 9(2012): 1569-1581. doi: 10.1109/TCBB.2012.124
   PubMed Web of Science ®Google Scholar
• L. Donetti, F. Neri and M. A. Muñoz, Optimal network topologies: Expanders, Cages, Ramanujan graphs, Entangled networks and all that, J. Stat. Mech. (2006) P08007.
   Google Scholar
• M. Daianu, N. Jahanshad, Talia M. Nir, Cassandra D. Leonardo, Clifford R. Jack Jr., Michael W. Weiner, Matthew A. Bernstein and Paul M. Thompson, Algebraic connectivity of brain networks shows patterns of segregation leading to reduced network robustness in Al-zheimer’s disease Comput Diffus MRI (2014): 5564. doi : 10.1007/978–3–319–11182–76.
   Google Scholar
• Wang X F and Chen G, Synchronization in small-world dynamical networks, Int. J. Bifurcation Chaos Appl. Sci. Eng. 12 187, 2002.
   Google Scholar
• Wang X F and Chen G, Synchronization in scale-free dynamical networks: robustness and fragility, IEEE Trans. Circ. Syst. I 49 54, 2002.
   Google Scholar
• P. Wei, G. Spiers and D. Sun, Algebraic Connectivity Maximization for Air Transportation Networks, IEEE Transactions on Intelligent Transportation Systems, 15, 2(2014): 685-698. doi: 10.1109/TITS.2013.2284913
   Web of Science ®Google Scholar
• H. Shakeri, N. Albin, F.D. Sahneh, P. Poggi-Corradini, and C. Scoglio, Maximizing algebraic connectivity in interconnected networks, Physical Review E 93(2016): 030301(R). doi: 10.1103/PhysRevE.93.030301
   PubMed Web of Science ®Google Scholar
• S. Fallat, S. Kirkland, S. Pati, Minimizing algebraic connectivity over connected graphs with fixed girth, Discrete Math. 254 (2002) 115-142. doi: 10.1016/S0012-365X(01)00355-7
   Web of Science ®Google Scholar
• J-M. Guo, W.C. Shiu, and J. Li. The algebraic connectivity of lollipop graph. Linear Algebra Appl., 434 (2011) 2204-2210. doi: 10.1016/j.laa.2010.12.020
   Web of Science ®Google Scholar
• W. C. Shiu, J.-M. Guo and J. Li, The minimum algebraic connectivity of caterpillar unicyclic graphs Electronic Journal of Linear Algebra, 22 (2011); 838-848.
   Google Scholar
• Y. Liu, Y. Liu, The ordering of unicyclic graphs with the smallest algebraic connectivity, Discrete Math., 309 (2009), 4315-4325. doi: 10.1016/j.disc.2009.01.010
   Web of Science ®Google Scholar
• J. Li, Ji-M. Guo, W. C. Shiu, The orderings of bicyclic graphs and connected graphs by algebraic connectivity, The electronic journal of combinatorics 17 (2010), 1-11.
   Web of Science ®Google Scholar
• C. Bu, and J. Zhou, Signless Laplacian spectral characterization of the cones over some regular graphs, Linear Algebra Appl., 436 (2012) 3634-3641. doi: 10.1016/j.laa.2011.12.035
   Web of Science ®Google Scholar
• X. Liu and P. Lu, Signless Laplacian spectral characterization of some joins, Electron. J. Linear Algebra., 30.1 (2015) 30. doi: 10.1016/j.laa.2015.01.040
   Google Scholar