5 problems

Let $c_d(n)$ denote the exponential growth constant for the maximum number of connected vertex subsets among $d$-regular graphs of order $n$. A Moore graph is a $d$-regular graph o…

Let $G_d$ be the radial Moore graph of degree $d$, and let the status of a vertex be the sum of its distances to all vertices of $G_d$. Maximal-status conjecture. The radial Moore…

Equatorial graph existence conjecture. There exists an equatorial graph with degree $\delta$ and girth $g$ if and only if there exists a Moore graph with degree $\delta$ and girth…

A $(d,g)$-Moore graph is a $d$-regular graph of girth $g$ with the Moore-bound number of vertices: … when $g$ is even, and … when $g$ is odd. Let $i(G)$ denote the total number of…

A $k$-regular graph $\Gamma$ of diameter $d$ and girth at least $2d-1$ is called a generalized Moore graph. Diameter conjecture. The diameter of a generalized Moore graph cannot ex…