5 problems

For every finite graph $G$ with order $n=|V(G)|$, size $m=|E(G)|$, and maximum degree $\Delta=\Delta(G)$, does the identifying vertex cover number of $G$ satisfy the upper-bound in…

Let $G$ be a connected identifiable graph of order $n\ge 2$ and maximum degree $\Delta\ge 2$. Write $\gamma^{{\rm ID}}(G)$ for the minimum size of an identifying code of $G$. Ident…

Let $G$ be a cubic graph, and let DET:IC%$(G)$ denote the minimum density of a deterministic error-detecting identifying code in $G$. Lower-bound conjecture. … The paper…

Let $C_n(1,3)$ be the circulant graph on vertex set $\mathbb{Z}_n$ in which vertices at cyclic distances $1$ or $3$ are adjacent. An identifying code is a dominating vertex set who…

Let $G$ be a twin-free graph, let $|V(G)|$ denote its number of vertices, and let $amma^{\text{\tiny{ID}}}(G)$ be its identifying code number. Write $\Delta(G)$ for the maximum deg…