The question asks for the equivalent resistance between $A$ and $B$, but the required circuit diagram is not present in the prompt.

Without the actual resistor network, the equivalent resistance cannot be determined uniquely, because different circuit connections can give different values such as $18\,\Omega$, $27\,\Omega$, $19\,\Omega$, or $25\,\Omega$.

What is missing

To solve such a problem, we need the circuit diagram showing:

1. How the resistors are connected between $A$ and $B$
2. The resistance values of each resistor
3. Any symmetry/bridge arrangement, if present

Therefore

Since the circuit is missing, a step-by-step calculation is not possible from the given information alone.

However, the stored correct answer is given as Option C, i.e. $19\,\Omega$

So the only answer we can report, based on the provided stored key, is: $R_{AB}=19\,\Omega$

But this cannot be independently verified without the circuit diagram.