Journal of Applied Mathematics

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

Xinying Pai and Sanyang Liu

Full-text: Open access

Abstract

Let Φ ( G , λ ) = d e t ( λ I n - L ( G ) ) = k = 0 n ( - 1 ) k c k ( G ) λ n - k be the characteristic polynomial of the Laplacian matrix of a graph G of order n . In this paper, we give four transforms on graphs that decrease all Laplacian coefficients c k ( G ) and investigate a conjecture A. Ilić and M. Ilić (2009) about the Laplacian coefficients of unicyclic graphs with n vertices and m pendent vertices. Finally, we determine the graph with the smallest Laplacian-like energy among all the unicyclic graphs with n vertices and m pendent vertices.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 404067, 11 pages.

Dates
First available in Project Euclid: 2 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.jam/1357153535

Digital Object Identifier
doi:10.1155/2012/404067

Mathematical Reviews number (MathSciNet)
MR2984200

Zentralblatt MATH identifier
1264.05082

Citation

Pai, Xinying; Liu, Sanyang. On the Laplacian Coefficients and Laplacian-Like Energy of Unicyclic Graphs with $n$ Vertices and $m$ Pendent Vertices. J. Appl. Math. 2012 (2012), Article ID 404067, 11 pages. doi:10.1155/2012/404067. https://projecteuclid.org/euclid.jam/1357153535


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