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Minimizing Laplacian spectral radius of unicyclic graphs with fixed girth

Kamal Lochan PatraBinod Kumar Sahoo — 2013

Czechoslovak Mathematical Journal

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 3 vertices. We prove that the graph U n , g uniquely minimizes the Laplacian spectral radius for n 2 g - 1 when g is even and for n 3 g - 1 when g is odd.

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