6 problems

For an integer $\ell\geq 1$, let $C^{\square}_{\ell}$ be the prism graph consisting of two vertex-disjoint $\ell$-cycles together with a perfect matching between corresponding vert…

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 $k\geq 1$ and $n\geq 1$. The stacked $(2k+1)$-gon prism graph $Y_{2k+1,n}$ consists of $n$ stacked copies of a $(2k+1)$-cycle prism. Let $\mathfrak{pr}(G)$ denote the minimum c…

For $n\geq 3$, let $GP(n,1)$ denote the prism graph on $2n$ vertices, and let $\mathfrak{pr}(G)$ be its minimum coprime number, the least maximum label in a coprime labeling. The p…

Let $G$ be a connected graph with $\operatorname{diam}(G)=2$, and let $\pi$ be a permutation of its vertex set $V_G$. Write $\gamma_{wcon}(G)$ for the weakly convex domination numb…

Let a prism constructed from an even-order cycle be the corresponding prism graph with cyclic base $C_n$ for even $n$. A graph is prime if it has a vertex labeling by consecutive i…