Abstract
The unicyclic graph Cn,gobtained by appending a cycle Cgof length g to a pendent vertex of a path on n - g vertices is the lollipop graph on n vertices. In [Algebraic connectivity of lollipop graphs, Linear Algebra Appl.434 (2011) 2204–2210], Guo et al. proved that a( Cn,g-1) < a( Cn,g) for g ≥ 4, where a( Cn,g) is the algebraic connectivity of Cn,g. In this paper, we present a new approach which is quite different from that of Guo et al. in proving a( Cn,g-1) < a( Cn,g) for g ≥ 4.
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