8 problems

Let $f_n(n)$ denote the spectral Nordhaus–Gaddum function defined in the paper for graphs of order $n$. Asymptotic conjecture for $f_n(n)$. … The paper proves the lower bound…

Let $f_1(n)$ denote the spectral Nordhaus–Gaddum function defined in the paper for graphs of order $n$. Asymptotic conjecture for $f_1(n)$. … The preceding construction gives the l…

Let $G$ be a graph on $n$ vertices, and let $\overline{G}$ denote its complement. Assume that both $G$ and $\overline{G}$ are connected; $\operatorname{Gap}(G)$ denotes the differe…

Let $G$ and $\overline{G}$ be nontrivial connected graphs of order $n\geq 8$. Write $rvd(G)$ for the rainbow vertex-disconnection number of $G$. Rainbow vertex-disconnection Nordha…

Let $G$ and $\overline{G}$ be complementary connected graphs with $n$ vertices. Ma's conjecture. There exist constants $C_1$ and $C_2$ such that … and this upper bound is tight. Th…

Let $G$ be a graph of order $n$, and let $\overline{G}$ denote its complement. Assume that every component of both $G$ and $\overline{G}$ has order at least $3$. Write…

Let $G$ range over graphs on $n$ vertices, let $\overline G$ be its complement, let $\mu(G)$ be the spectral radius, and let $s^+(G)$ be the sum of the squares of the positive adja…

Let $G_1,\ldots,G_r$ be graphs on a common vertex set of size $n$, whose edge sets partition the edges of $K_n$, and let $\ngpl{\eta}(r;n)$ denote the minimum of…