Table 1 The Euler characteristic \(\chi \) and the generalized Euler characteristic \(\chi _{G}\) predicted for the microwave networks \(\Gamma (6,8,|V_D|=0,1,2)\) for four combinations of Neumann (N) and Dirichlet (D) boundary conditions (BC) on the two tail-like edges \(l_{2,5}\) and \(l_{4,6}\).
\(\text{ BC: } l_{2,5}\) | \(\text{ BC: } l_{4,6}\) | \(\;\;\; \chi \;\;\;\) | \(\;\; \chi _G \;\; \) |
|---|---|---|---|
N | N | \(-2\) | − |
N | D | − | \(-3\) |
D | N | − | \(-3\) |
D | D | − | \(-4\) |
