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].
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