3 problems

Let $P_n$ and $C_n$ denote, respectively, the path and cycle on $n$ vertices, and let $\rho_R(G)$ denote the replication number of a graph $G$. The cycle–path replication conjectur…

Let $P_n$ be the path on $n$ vertices, and let $\rho_R(P_n)$ denote its replication number. The notation $O(n)$ means a quantity bounded in absolute value by a constant multiple of…

Let $P_n$ be the path on $n$ vertices, and let $\rho_R(P_n)$ denote its replication number. For odd $n\geq 1$, write the upper-bound formula according to the residue class of $n$ m…