On Properties of a Graph that Depend on its Distance Function
✍ Scribed by Ladislav Nebeský
- Book ID
- 111577435
- Publisher
- Springer
- Year
- 2004
- Tongue
- English
- Weight
- 127 KB
- Volume
- 54
- Category
- Article
- ISSN
- 0011-4642
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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 _
The average n-distance of a connected graph G, p,,(G), is the average of the Steiner distances of all n-sets of vertices of G. In this paper, we give bounds on pn for two-connected graphs and for k-chromatic graphs. Moreover, we show that pn(G) does not depend on the n-diameter of G.