An Optimality Criterion and the Total Length of the Graph Realization of a Distance Matrix
✍ Scribed by J. M. S. SIMÕES–PEREIRA
- Book ID
- 119863035
- Publisher
- John Wiley and Sons
- Year
- 1989
- Tongue
- English
- Weight
- 391 KB
- Volume
- 555
- Category
- Article
- ISSN
- 0890-6564
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## 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 _
Recently, several results bounding above the diameter and/or the mean distance of a graph from its eigenvalues have been presented. They use the eigenvalues of either the adjacency or the Laplacian matrix of the graph. The main object of this paper is to compare both methods. As expected, they are e