5 problems

Anđelić–da Fonseca–Simić–Du conjecture. There do not exist non-isomorphic cospectral connected chain graphs with respect to the adjacency spectrum.

Let $G$ be a chain graph of order $n$ with binary string … where … and $s_i\geq 1$ and $t_i\geq 1$ for $1\leq i\leq k$. Let $SE(G)$ denote the Seidel energy, and let…

Let $(G_n)_{n \geq 1}$ be a family of linked chain graphs with linking permutations $\pi_1,\pi_2,\dots$, and let $\mathcal X$ be the hereditary closure of this family. Write…

Downer-vertex conjecture. In any chain graph, every vertex is downer with respect to every non-zero eigenvalue.

Alazemi–Andelić–Simić conjecture. In any chain graph, every vertex is downer with respect to every non-zero eigenvalue. Equivalently, for every chain graph $G$, every $v\in V(G)$,…