Graph decompositions in projective geometries

Marco Buratti, Anamari Nakic, Alfred Wassermann

Let PG$({\mathbb{F}}_q^v)$ be the $(v-1)$-dimensional projective space over ${\mathbb{F}}_q$ and let $\Gamma$ be a simple graph of order $\frac{q^k-1}{q-1}$ for some $k$. A 2$-(v,\Gamma ,\lambda )$ desig…