Reliability Analysis of the Cayley Graphs of Dihedral Groups

Cayley graphs have many good properties as models of communication networks. This study analyzes the reliability of the Cayley graph based on the dihedral graph. Graph theory and analyses show that almost all Cayley graphs of the dihedral graph $D_{2n}$ are optimal super-λ. The number $N_i(G)$ of cutsets of size $i,\lambda ⩽i⩽{\lambda }^{\mathrm{\prime }}$ is given as $N_i(G)=n(\genfrac{}{}{0ex}{}{(n-1)\delta }{i-\delta })$.