Department of Mathematics
The algebraic connectivity of lollipop graphs
Let Cn,g be the lollipop graph obtained by appending a g-cycle Cg to a pendant vertex of a path on n-g vertices. In 2002, Fallat, Kirkland and Pati proved that for n≥3g-12 and g≥4, α(Cn,g)>α(Cn,g-1). In this paper, we prove that for g≥4, α(Cn,g)>α(Cn,g-1) for all n, where α(Cn,g) is the algebraic connectivity of Cn,g. © 2010 Elsevier Inc. All rights reserved.
Algebraic connectivity, Characteristic polynomial, Lollipop graph
Source Publication Title
Linear Algebra and its Applications
Link to Publisher's Edition
Guo, J., Shiu, W., & Li, J. (2011). The algebraic connectivity of lollipop graphs. Linear Algebra and its Applications, 434 (10), 2204-2210. https://doi.org/10.1016/j.laa.2010.12.020