%0 Journal Article
%T On the Laplacian Coefficients and Laplacian-Like Energy of Unicyclic Graphs with  Vertices and  Pendent Vertices
%A Xinying Pai
%A Sanyang Liu
%J Journal of Applied Mathematics
%D 2012
%I Hindawi Publishing Corporation
%R 10.1155/2012/404067
%X 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. Ilić and M. Ilić (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.
%U http://www.hindawi.com/journals/jam/2012/404067/