Abstract
Let G (n, k, t) be a set of graphs with n vertices, k cut edges and t cut vertices. In this paper, we classify these graphs in G (n, k, t) according to cut vertices, and characterize the extremal graphs with the largest spectral radius in G (n, k, t).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Berman, A., Zhang, X.-D.: On the spectral radius of graphs with cut vertices. J. Combin. Theory Ser. B, 83, 233–240 (2001)
Bondy, J. A., Murty, U. S. R.: Graph Theory with Applications, The Macmillan Press LTD, London, 1976
Bruadli, R. A., Solheid, E. S.: On the spectral radius of complementary acyclic matrices of zeros and ones. SIAM J. Algebra Discrete Methods, 7, 265–272 (1986)
Cvetković, D., Rowlinson, P., Simić, S.: Eigenspaces of Graphs, Cambridge University Press, Cambridge, 1997
Guo, S. Q.: First six unicyclic graphs of order n with larger spectral radius (in Chinese). Appl. Math. J. Chinese Univ. Ser. A, 18(4), 480–486 (2003)
Li, Q., Feng, K.: On the largest eigenvalue of a graph (in Chinese). Acta Math. Appl. Sinica, 2, 167–175 (1979)
Liu, H. Q., Lu, M., Tian, F.: On the spectral radius of graphs with cut edges. Linear Algebra Appl., 389, 139–145 (2004)
Wu, B. F., Xiao, E. L., Yuan, H.: The spectral radius of trees on k pendent vertices. Linear Algebra Appl., 395, 343–349 (2005)
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by National Natural Science Foundation of China (Grant No. 11071078)
Rights and permissions
About this article
Cite this article
Fang, K.F., Shu, J.L. On graphs with cut vertices and cut edges. Acta. Math. Sin.-English Ser. 30, 539–546 (2014). https://doi.org/10.1007/s10114-014-1230-z
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10114-014-1230-z