6 problems

A prime labeling of a graph $G$ is a bijection from $V(G)$ to $\{1,2,\ldots,|V(G)|\}$ such that adjacent vertices receive relatively prime labels. The tree prime-labeling conjectur…

A prism graph is the Cartesian product $P_2\square C_n$ of a path on two vertices and a cycle of length $n$. A graph is prime if its vertices can be bijectively labeled with…

Let $L_n=P_2\times P_n$ be the ladder graph of order $2n$. A graph is prime when its vertices can be bijectively labeled by $\{1,2,\ldots,m\}$, where $m$ is its order, so that adja…

Deretsky–Lee–Miller conjecture. Every union of cycles with at most one odd cycle has a prime labeling.

A graph of order $N$ is prime if its vertices can be labeled with the distinct integers $1,\ldots,N$ so that adjacent vertices receive relatively prime labels. A graph's minimum co…

A tree is a connected graph with no cycles, and a graph of order $n$ is prime if its vertices can be labeled with the distinct integers $1,\ldots,n$ so that adjacent vertices recei…