Department of Mathematics
The smallest values of algebraic connectivity for unicyclic graphs
The algebraic connectivity of G is the second smallest eigenvalue of its Laplacian matrix. Let un 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]. © 2010 Elsevier B.V. All rights reserved.
Algebraic connectivity, Order, Unicyclic graph
Source Publication Title
Discrete Applied Mathematics
Li, Jianxi, Ji-Ming Guo, and Wai Chee Shiu. "The smallest values of algebraic connectivity for unicyclic graphs." Discrete Applied Mathematics 158.15 (2010): 1633-1643.