Simultaneous coloring of vertices and incidences of hypercubes

An element $i=(v,e)$ of a graph $G$ is called  an incidence of $G$, if $v\in V(G)$, $e\in E(G)$ and $v\in e$. The simultaneous coloring of vertices and incidences of a graph is coloring  the vertices and incidences of the graph properly at the same time such that any two adjacent or incident elements receive distinct colors. In this paper, we investigate the simultaneous coloring of vertices and incidences of hypercubes.