From two graphs $G_1$ and $G_2$ on $N_1$ and $N_2$ vertices respectively, the compound graph $G_1[G_2]$ on $N_1N_2$ vertices is obtained connecting $N_2$ copies of $G_1$ following the structure of $G_2$. We present in this paper methods of compounding that result in families of graphs with large number of vertices for given values of the maximum degree $\Delta$ and diameter $D$.

Peer Reviewed