The smallest values of algebraic connectivity for unicyclic graphs

  • Authors:

  • Jianxi Li;Ji-Ming Guo;Wai Chee Shiu

  • Affiliations:

  • Department of Mathematics and Information Science, Zhangzhou Normal University, Zhangzhou, Fujian, China and Department of Mathematics, Hong Kong Baptist University, 224 Waterloo Road, Kowloon Ton ...;Department of Applied Mathematics, China University of Petroleum, Dongying, Shandong, China;Department of Mathematics, Hong Kong Baptist University, 224 Waterloo Road, Kowloon Tong, Hong Kong, China

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2010

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Abstract

The algebraic connectivity of G is the second smallest eigenvalue of its Laplacian matrix. Let U"n be the set of all unicyclic graphs of order n. In this paper, we will provide the ordering of unicyclic graphs in U"n up to the last seven graphs according to their algebraic connectivities when n=13. This extends the results of Liu and Liu [Y. Liu, Y. Liu, The ordering of unicyclic graphs with the smallest algebraic connectivity, Discrete Math. 309 (2009) 4315-4325] and Guo [J.-M. Guo, A conjecture on the algebraic connectivity of connected graphs with fixed girth, Discrete Math. 308 (2008) 5702-5711].