# Bled'11 - 7th Slovenian International Conference on Graph Theory

19-25 June 2011
Bled, Slovenia
Europe/Ljubljana timezone
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# A new inequality for distance-regular graphs

Presented by Dr. Jernej TONEJC
Type: Oral presentation
Track: Representations of Graphs

## Content

We will prove a new inequality for distance-regular graphs with diameter $d\geqslant 3$. Further, we will show that equality holds in several important cases, among others for antipodal distance-regular graphs (both nonbipartite and bipartite). Using this new inequality we will show that an infinite family of feasible intersection arrays given by $$\left\{ \frac{( q^2 - 2)(q+1)}{2}, \frac{(q-1)^2 (q+2)}{2}, \frac{q(q-1)}{2}; 1, \frac{(q-1) (q+2)}{2}, \frac{(q-1) q (q+1)}{2}\right\}$$ cannot exist.

## Place

Location: Bled, Slovenia
Address: Best Western Hotel Kompas Bled

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