3 problems

Akbari–Cameron–Khosrovshahi conjecture. There exists a nonzero ${0,1}$-vector in the row space of $A_G$ that is not one of the rows of $A_G$.

Let $k\ge 2$ and $d_1,d_2,\ldots,d_{k-1}$ be integers of at least $2$. A generalized Bethe tree $\mathcal{B}(d_1,d_2,\ldots,d_{k-1})$ with $k$ levels is a rooted tree in which all…

Let $H$ be a graph whose adjacency matrix is singular. Vertices of $H$ are said to have the same neighborhood when they are adjacent to exactly the same vertices. Generic-singulari…