The (signless) Laplacian spectral radii of c-cyclic graphs with n vertices, girth g and k pendant vertices

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].

Keywords:

• c-cyclic graph
• girth
• pendant vertices
• adjacency spectral radius
• (signless) Laplacian spectral radius

AMS Subject Classifications:

• 05C50
• 05C35
• 05C75

Acknowledgements

The authors would like to thank the referees for their valuable comments, corrections and suggestions, which lead to an improvement of the original manuscript.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author is partially supported by NSFC project [grant number 11571123], the Training Program for Outstanding Young Teachers in University of Guangdong Province [grant number YQ2015027]; China Scholarship Council, and the second author is partially supported by the National Research Foundation funded by the Korean government with the [grant number 2013R1A1A2009341].