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JOURNAL OF
ALGEBRAIC
COMBINATORICS
  Editors-in-chief: C. A. Athanasiadis, T. Lam, A. Munemasa, H. Van Maldeghem
ISSN 0925-9899 (print) • ISSN 1572-9192 (electronic)
 

Tight Graphs and Their Primitive Idempotents

Arlene A. Pascasio
De La Salle University Mathematics Department Manila 1004 Philippines

DOI: 10.1023/A:1018624103247

Abstract

In this paper, we prove the following two theorems.
Theorem 1 Let s i r i - s i - 1 r i - 1 = Ĩ ( s i - 1 r i - s i r i - 1 ) (1 \leqslant i \leqslant d). σ_i ρ_i - σ_{i - 1} ρ_{i - 1} = \in (σ_{i - 1} ρ_i - σ_i ρ_{i - 1} ) (1 \leqslant i \leqslant d). Let $\begin{gathered} \underset{\raise0.3em\hbox{$ \begin{gathered} \underset{\raise0.3em\hbox{
They defined Gamma to be tight whenever Gamma is not bipartite, and equality holds above.

Pages: 47–59

Keywords: tight graph; distance-regular; association scheme; Kreĭn parameter

Full Text: PDF

References

E. Bannai and T. Ito, Algebraic Combinatorics I: Association Schemes, Benjamin-Cummings Lecture Note Ser. 58, Benjamin-Cummings, Menlo Park, CA.
1984. A.E. Brouwer, A.M. Cohen, and A. Neumaier, Distance-Regular Graphs, Springer, New York,
1989. C.D. Godsil, Algebraic Combinatorics, Chapman and Hall, New York,
1993. A. Juri i , J. Koolen, and P. Terwilliger, Tight distance-regular graphs, submitted.



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