The Laplacian spread of quasi-tree graphs
โ Scribed by Ying Xu; Jixiang Meng
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 191 KB
- Volume
- 435
- Category
- Article
- ISSN
- 0024-3795
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๐ SIMILAR VOLUMES
The Laplacian spread s(G) of a graph G is defined to be the difference between the largest eigenvalue and the second-smallest eigenvalue of the Laplacian matrix of G. Several upper bounds of Laplacian spread and corresponding extremal graphs are obtained in this paper. Particularly, if G is a conne
be the Laplacian matrix of G. When G is a tree or a bipartite graph we obtain bounds for the permanent of L(G) both in terms of n only and in terms of d 1 ..... d,. Improved bounds are obtained in terms of the diameter of T and the size of a matching in T.
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