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

Let Φ(G,λ)=det(λIn-L(G))=∑k=0n(-1)kck(G)λn-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 ck(G) and investigate a conjecture A. Ilić and M. Ilić (2009) about the Laplacian c...

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Main Authors:	Xinying Pai, Sanyang Liu
Format:	Article
Language:	English
Published:	Hindawi Limited 2012-01-01
Series:	Journal of Applied Mathematics
Online Access:	http://dx.doi.org/10.1155/2012/404067

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spelling	doaj-a5755d7ea18943f08924a2c6012f61d12020-11-24T22:51:20ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/404067404067On the Laplacian Coefficients and Laplacian-Like Energy of Unicyclic Graphs with n Vertices and m Pendent VerticesXinying Pai0Sanyang Liu1Department of Mathematics, Xidian University, Shanxi Xi'an 710071, ChinaDepartment of Mathematics, Xidian University, Shanxi Xi'an 710071, ChinaLet Φ(G,λ)=det(λIn-L(G))=∑k=0n(-1)kck(G)λn-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 ck(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.http://dx.doi.org/10.1155/2012/404067
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Xinying Pai Sanyang Liu
spellingShingle	Xinying Pai Sanyang Liu On the Laplacian Coefficients and Laplacian-Like Energy of Unicyclic Graphs with n Vertices and m Pendent Vertices Journal of Applied Mathematics
author_facet	Xinying Pai Sanyang Liu
author_sort	Xinying Pai
title	On the Laplacian Coefficients and Laplacian-Like Energy of Unicyclic Graphs with n Vertices and m Pendent Vertices
title_short	On the Laplacian Coefficients and Laplacian-Like Energy of Unicyclic Graphs with n Vertices and m Pendent Vertices
title_full	On the Laplacian Coefficients and Laplacian-Like Energy of Unicyclic Graphs with n Vertices and m Pendent Vertices
title_fullStr	On the Laplacian Coefficients and Laplacian-Like Energy of Unicyclic Graphs with n Vertices and m Pendent Vertices
title_full_unstemmed	On the Laplacian Coefficients and Laplacian-Like Energy of Unicyclic Graphs with n Vertices and m Pendent Vertices
title_sort	on the laplacian coefficients and laplacian-like energy of unicyclic graphs with n vertices and m pendent vertices
publisher	Hindawi Limited
series	Journal of Applied Mathematics
issn	1110-757X 1687-0042
publishDate	2012-01-01
description	Let Φ(G,λ)=det(λIn-L(G))=∑k=0n(-1)kck(G)λn-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 ck(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.
url	http://dx.doi.org/10.1155/2012/404067
work_keys_str_mv	AT xinyingpai onthelaplaciancoefficientsandlaplacianlikeenergyofunicyclicgraphswithnverticesandmpendentvertices AT sanyangliu onthelaplaciancoefficientsandlaplacianlikeenergyofunicyclicgraphswithnverticesandmpendentvertices
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On the Laplacian Coefficients and Laplacian-Like Energy of Unicyclic Graphs with n Vertices and m Pendent Vertices

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