I want to communicate between two arduino's using one wire (sending and receiving signals - if matched, blink LED by receiver to indicate it), which are separately powered by 9v batteries.
I want to send only just a signal (as a CLK).
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One wire does nothing.
For transmitting power or signal you need a voltage differential, and that means two wires minimum. One wire is for ground, a common base level for the two Arduinos. The other is for the signal itself.
In some cases (cars) you only see one wire connecting things, but the car frame itself is uses as ground.
Edit: This blog The Importance of Sharing Grounds explain the matter in great detail.