Kaleidoscopic graphs

Let $\rm Gr=({\cal V}, E)$ be a connected graph with a set of vertices ${\cal V}$ and a set of edges $E$, $B(x,1)=\{y\in {\cal V}:(x,y)\in E\}\cup \{x\},$ $x\in {\cal V}.$ A graph $\rm Gr=({\cal V}, E)$ is called kaleidoscopic if there exist a natural number $s>1$ and a $(s+1)$-coloring of ${\cal V}$ such that $|B(x,1)|=s+1$ and $B(x,1)$ contains the vertices of all colors for every $x\in {\cal V}.$ We present two methods for construction of kaleidoscopic graphs based on the Cayley graphs of the groups.