On the Laplacian Coefficients and Laplacian-Like Energy of Unicyclic Graphs with Vertices and Pendent Vertices

Xinying Pai and Sanyang Liu

Journal of Applied Mathematics, 2012, vol. 2012, 1-11

Abstract:

Let be the characteristic polynomial of the Laplacian matrix of a graph of order . In this paper, we give four transforms on graphs that decrease all Laplacian coefficients and investigate a conjecture A. Ilic and M. Ilic (2009) about the Laplacian coefficients of unicyclic graphs with vertices and pendent vertices. Finally, we determine the graph with the smallest Laplacian-like energy among all the unicyclic graphs with vertices and pendent vertices.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:404067

DOI: 10.1155/2012/404067

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