TY - JOUR
T1 - The smallest values of algebraic connectivity for unicyclic graphs
AU - Li, Jianxi
AU - Guo, Ji Ming
AU - SHIU, Wai Chee
N1 - Funding Information:
Partially supported by FRG, Hong Kong Baptist University (No. FRG2/08-09/63 ); the National Science Foundation of China (No. 10871204 ) and the Fundamental Research Funds for the Central Universities (No. 09CX04003A ).
PY - 2010/8/6
Y1 - 2010/8/6
N2 - 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].
AB - 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].
KW - Algebraic connectivity
KW - Order
KW - Unicyclic graph
UR - http://www.scopus.com/inward/record.url?scp=77955423508&partnerID=8YFLogxK
U2 - 10.1016/j.dam.2010.05.009
DO - 10.1016/j.dam.2010.05.009
M3 - Article
AN - SCOPUS:77955423508
VL - 158
SP - 1633
EP - 1643
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
SN - 0166-218X
IS - 15
ER -