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].
Scopus Subject Areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics
- Algebraic connectivity
- Unicyclic graph