Geodesic
Minimizing Laplacian spectral radius of unicyclic graphs with fixed girth
Czechoslovak Mathematical Journal, Tome 63 (2013) no. 4, pp. 909-922.

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In this paper we consider the following problem: Over the class of all simple connected unicyclic graphs on $n$ vertices with girth $g$ ($n$, $g$ being fixed), which graph minimizes the Laplacian spectral radius? Let $U_{n,g}$ be the lollipop graph obtained by appending a pendent vertex of a path on $n-g$ $(n> g)$ vertices to a vertex of a cycle on $g\geq 3$ vertices. We prove that the graph $U_{n,g}$ uniquely minimizes the Laplacian spectral radius for $n\geq 2g-1$ when $g$ is even and for $n\geq 3g-1$ when $g$ is odd.
DOI : 10.1007/s10587-013-0061-x
Classification : 05C50
Keywords: Laplacian matrix; Laplacian spectral radius; girth; unicyclic graph 
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     title = {Minimizing {Laplacian} spectral radius of unicyclic graphs with fixed girth},
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Patra, Kamal Lochan; Sahoo, Binod Kumar. Minimizing Laplacian spectral radius of unicyclic graphs with fixed girth. Czechoslovak Mathematical Journal, Tome 63 (2013) no. 4, pp. 909-922. doi : 10.1007/s10587-013-0061-x. http://geodesic.mathdoc.fr/articles/10.1007/s10587-013-0061-x/

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