5 problems

Let $G$ and $H$ be graphs, and suppose that a single similarity matrix establishes cospectrality of their generalized distance matrices for two distinct values of $q$, neither of w…

Let $G_1$ and $G_2$ be graphs with $B_1\subseteq V(G_1)$ and $B_2\subseteq V(G_2)$. Coalescing conjecture. If coalescing the same connected rooted graph onto every vertex of $B_1$…

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

Let $K_w$ be the complete graph on $w$ vertices, let $C_n$ be the cycle graph on $n$ vertices, and let $mC_n$ denote the disjoint union of $m$ copies of $C_n$. Write…

For integers $p$ and $q$ with $q>2$, let $Kite_{p,q}$ denote the graph obtained by appending a complete graph $K_p$ to a pendant vertex of a path $P_q$. A graph is determined by ad…