✦ LIBER ✦

Two Laplacians for the distance matrix of a graph

✍ Scribed by Aouchiche, Mustapha; Hansen, Pierre

Book ID: 120570769
Publisher: Elsevier Science
Year: 2013
Tongue: English
Weight: 822 KB
Volume: 439
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2013.02.030

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

Distance matrix and Laplacian of a tree

Distance matrix and Laplacian of a tree with attached graphs

✍ R.B. Bapat 📂 Article 📅 2005 🏛 Elsevier Science 🌐 English ⚖ 172 KB

A tree with attached graphs is a tree, together with graphs defined on its partite sets. We introduce the notion of incidence matrix, Laplacian and distance matrix for a tree with attached graphs. Formulas are obtained for the minors of the incidence matrix and the Laplacian, and for the inverse and

The laplacian matrix of a graph: unimodu

The laplacian matrix of a graph: unimodular congruence

✍ Watkins, William 📂 Article 📅 1990 🏛 Taylor and Francis Group 🌐 English ⚖ 933 KB

Unimodular congruence of the Laplacian m

Unimodular congruence of the Laplacian matrix of a graph

✍ William Watkins 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 609 KB

On the distance matrix of a directed gra

On the distance matrix of a directed graph

✍ R. L. Graham; A. J. Hoffman; H. Hosoya 📂 Article 📅 1977 🏛 John Wiley and Sons 🌐 English ⚖ 144 KB 👁 2 views

## Abstract In this note, we show how the determinant of the distance matrix __D(G__) of a weighted, directed graph __G__ can be explicitly expressed in terms of the corresponding determinants for the (strong) blocks __G~i~__ of __G__. In particular, when cof __D(G__), the sum of the cofactors of _

The Laplacian lattice of a graph under a

The Laplacian lattice of a graph under a simplicial distance function

✍ Manjunath, Madhusudan 📂 Article 📅 2013 🏛 Elsevier Science 🌐 English ⚖ 529 KB

A new upper bound for eigenvalues of the

A new upper bound for eigenvalues of the laplacian matrix of a graph

✍ Li Jiong-Sheng; Zhang Xiao-Dong 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 270 KB

We first give a result on eigenvalues of the line graph of a graph. We then use the result to present a new upper bound for eigenvalues of the Laplacian matrix of a graph. Moreover we determine all graphs the largest eigenvalue of whose Laplacian matrix reaches the upper bound.