Bapat, R. B. ; Kirkland, S. J. ; Pati, S.
(2001)
*The perturbed Laplacian matrix of a graph*
Linear and Multilinear Algebra, 49
(3).
pp. 219-242.
ISSN 0308-1087

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Official URL: http://www.tandfonline.com/doi/abs/10.1080/0308108...

Related URL: http://dx.doi.org/10.1080/03081080108818697

## Abstract

For a graph G, we define its perturbed Laplacian matrix as D-A(G) where A(G) is the adjacency matrix of G and D is an arbitrary diagonal matrix. Both the Laplacian matrix and the negative of the adjacency matrix are special instances of the perturbed Laplacian. Several well-known results, contained in the classical work of Fiedler and in more recent contributions of other authors are shown to be true, with suitable modifications, for the perturbed Laplacian. An appropriate generalization of the monotonicity property of a Fiedler vector for a tree is obtained. Some of the results are applied to interval graphs.

Item Type: | Article |
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Source: | Copyright of this article belongs to Taylor and Francis Group. |

Keywords: | Laplacian Matrix; Algebraic Connectivity; Characteristic Set; Interval Graphs; Perturbed Laplacian Matrix; Fiedler Vector; Perron Component |

ID Code: | 77912 |

Deposited On: | 14 Jan 2012 15:41 |

Last Modified: | 14 Jan 2012 15:41 |

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