## 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 _
โฆ LIBER โฆ
Distance-regular Graphs the Distance Matrix of which has Only One Positive Eigenvalue
โ Scribed by J.H. Koolen; S.V. Shpectorov
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 244 KB
- Volume
- 15
- Category
- Article
- ISSN
- 0195-6698
No coin nor oath required. For personal study only.
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and Terwilliger recently introduced the notion of a tridiagonal pair. We apply their results to distance-regular graphs and obtain the following theorem. THEOREM. Let denote a distance-regular graph with diameter D โฅ 3. Suppose is Q-polynomial with respect to the ordering E 0 , E 1 , . . . , E D of