An edge-colored graph is rainbow if no two edges of the graph have the same color. A strongly edge-colored graph is an edge-colored graph such that every path of length 3 is rainbow. We call an edge-colored graph G c is rainbow vertex pairpancyclic if any two vertices in G c are contained in a rainbow cycle of length l for each l with 3 ≤ l ≤ n. In this paper, we show that every strongly edge-colored graph G c of order n with minimum degree δ ≥ 2n 3 + 1 is rainbow vertex pair-pancyclicity.

An edge-colored graph is \emph{rainbow }if no two edges of the graph have the same color. An edge-colored graph $G^c$ is called \emph{properly colored} if every two adjacent edges of $G^c$ receive distinct colors in $G^c$. A \emph{strongly edge-colored} graph is a proper edge-colored graph such that every path of length $3$ is rainbow. We call an edge-colored graph $G^c$ \emph{rainbow vertex pair-pancyclic} if any two vertices in $G^c$ are contained in a rainbow cycle of length $\ell$ for each $\ell$ with $3 \leq \ell \leq n$. In this paper, we show that every strongly edge-colored graph $G^c$ of order $n$ with minimum degree $\delta \geq \frac{2n}{3}+1$ is rainbow vertex pair-pancyclicity.