Tight Graphs and Their Primitive Idempotents(Groups and Combinatorics)
Arlene A. Pascasio · Institutional Repositories DataBase (IRDB) · 1997
In this paper, we prove Theorem 1.Let $\Gamma$ denote a distance-regular graph with diameter $d\geq 3$ .Sup- pose $E$ and $F$ are primitive idempotents of $\Gamma$ , with cosine sequences $\sigma_{0},$ $\sigma_{1,\ldots,d}\sigma$ and $\rho_{0},$ $\rho_{1},$ $\ldots,\rho_{d}$ , respectively.Then the following are equivalent.i) The entry-wise product $E\circ F$ is a scalar multiple of a primitive idempotent of $\Gamma$ .