Abstract
Let denote the class of c-cyclic graphs with n vertices, girth and pendant vertices. In this paper, we determine the unique extremal graph with largest signless Laplacian spectral radius and Laplacian spectral radius in the class of connected c-cyclic graphs with vertices, girth g and at most pendant vertices, respectively, and the unique extremal graph with largest signless Laplacian spectral radius of when and , and we also identify the unique extremal graph with largest Laplacian spectral radius in in the case and either and g is even or and g is odd. Our results extends the corresponding results of [Sci. Sin. Math. 2010;40:1017–1024, Electron. J. Combin. 2011; 18:p.183, Comput. Math. Appl. 2010;59:376–381, Electron. J. Linear Algebra. 2011;22:378–388 and J. Math. Res. Appl. 2014;34:379–391].
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