Minimizing Laplacian spectral radius of unicyclic graphs with fixed girth
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 Un,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 Un,g uniquely minimizes the Laplacian spectral radius for n ⩾ 2g − 1 when g is even and for n ⩾ 3g − 1 when g is odd.
KeywordsLaplacian matrix Laplacian spectral radius girth unicyclic graph
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- B. Mohar: The Laplacian spectrum of graphs. Graph Theory, Combinatorics and Applications, Kalamazoo, MI, 1988, Vol. 2 (Alavi, Y., ed.). Wiley-Intersci. Publ., Wiley, New York, 1991, pp. 871–898.Google Scholar