1,699
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Leading eigenvalues of adjacency matrices of star-like graphs with fixed numbers of vertices and edges

& | (Reviewing editor)
Article: 1628513 | Received 06 Aug 2018, Published online: 18 Jun 2019

References

  • Berman, A., & Plemmons, R. J. (1994). Nonnegative matrices in the mathematical sciences (pp. 27). Philadelphia: SIAM.
  • Brauer, F. (2008). An introduction to networks in epidemic modeling. In Mathematical epidemiology (pp. 133–8). Lecture Notes in Math., 1945, Math. Biosci. Subser.,  Berlin: Springer.
  • Brouwer, A. E., & Haemers, W. H. (2010). Spectra of graphs (pp. 33). New York, Dordrecht, Heidelberg and London: Spinger.
  • Brualdi, R. A., & Hoffman, A. J. (1985). On the spectral radius of (0,1)-matrices. Linear Algebra and Its Applications, 65, 133–146. doi:10.1016/0024-3795(85)90092-8
  • Bunimovich, L., & Webb, B. (2014). Isospectral transformations (pp. 20). New York: Springer.
  • Del-Vecchio, R. R., Gutman, I., Trevisan, V., & Vinagre, C. T. M. (2009). On the spectral and energies of double-broom-like trees. Kragujevac Journal of Science, 31, 45–58.
  • Diekmann, O., & Heesterbeek, J. (2000). Mathematical epidemiology of infectious diseases: Model building, analysis and interpretation (pp. 73–77). Chichester: John Wiley.
  • Gatto, M., Mari, L., & Rinaldo, A. (2013, Sept). Leading eigenvalues and the spread of cholera. SIAM News, 43, 3.
  • Hoffman, A. J. (1972). On limit points of spectral radii of non-negative symmetric integral matrices. In Graph theory and applications (Vol. 303, pp. 165–172). Lecture Notes in Math. Berlin: Springer.
  • Jiang, M. (2016). Approximating individual risk of infection in a markov chain epidemic network model with a deterministic system. Journal of Difference Equations Applications, 22(10), 1438–1451. doi:10.1080/10236198.2016.1201476
  • Kostova, T. (2009). Interplay of node connectivity and epidemic rates in the dynamics of epidemic networks. Journal of Difference Equations Applications, 15(4), 415–428. doi:10.1080/10236190902766835
  • Kulkarni, D., Schmidt, D., & Tsui, S.-K. (1999). Eigenvalues of tridiagonal pseduo-teoplitz matrices. Linear Algebra and Its Applications, 297(1), 63–80. doi:10.1016/S0024-3795(99)00114-7
  • Li, Q., & Feng, K. Q. (1979). On the largest eigenvalue of a graph (Chinese). Acta Mathematicae Applicatae Sinica, 2(2), 157–175.
  • Liu, H., Lu, M., & Tian, F. (2004). On the spectral radius of graphs with cut edges. Linear Algebra and Its Applications, 389(Supplement C), 139–145. doi:10.1016/j.laa.2004.03.026
  • Newman, M. (2002, Jul). Spread of epidemic disease on networks. Physical Review E, 66, 016128. doi:10.1103/PhysRevE.66.016128
  • Newman, M. (2010). Networks, an introduction (pp. 591). New York, NY, USA: Oxford University Press, Inc.
  • Patuzzi, L., de Freitas, M., & Del-Vecchio, R. R. (2014). Indices for special classes of trees. Linear Algebra and Its Applications, 442, 106–114. doi:10.1016/j.laa.2013.07.007