10 problems

Two-thirds conjecture. Every twin-free isolate-free graph $G$ of order $n$ satisfies

Garijo's conjecture.

A graph $G$ is twin-free if no two vertices have the same open or closed neighbourhood. Let $\gamma_{LD}(G)$ denote the locating-dominating number of $G$, the minimum cardinality o…

Let $G$ be a finite graph. A set $C\subseteq V(G)$ is a locating-dominating set if it dominates every vertex outside $C$ and, for every two distinct vertices…

Location-domination conjecture. If $G$ is a twin-free graph on $n$ vertices, then

Let $K$ denote the infinite king grid, and let $\operatorname{DET:LD}(K)$ denote its deterministic locating-dominating density. Deterministic locating-dominating density conjecture…

Let $G$ be a twin-free graph of order $n$, and let a locating-dominating set be a set of vertices that is both locating and dominating. Write $\gamma^{LD}(G)$ for the minimum size…

Let $D$ be a twin-free digraph of order $n$, and let $\gamma^{LD}(D)$ denote the minimum size of a locating-dominating set of $D$. Foucaud, Heydarshahi and Parreau proved…

Let $G$ be a graph of order $n$ with no isolated vertices. A graph is twin-free if no two distinct vertices have the same open or closed neighborhood, and let $\gamma_L(G)$ be its…

For a graph $G$, let $\dim(G)$ denote its metric dimension, $\lambda(G)$ its locating-dominating number, and $\operatorname{Det}(G)$ its distinguishing number. For each positive in…