By strobing I suppose you mean...
(a) flashing each led for a brief instant,
(b) multiplexing the led's in rotation?
An easy way to do item B is to use a 4017 IC (1-through-10 sequencer).
It rotates a clock signal through 10 output pins.
You probably want to light each led for a brief instant. (Item A above.)
Your led draws 1A at 36V. It might require 30V to turn on. Suppose you put a capacitor in series. It will pass full current to light the led brightly for a fraction of a second. When the capacitor has acquired a few volts of charge, the led drops below 30V and goes dim. This is the brief strobe effect. The flash captures the eye's attention, while drawing minimal power.
During idle time, a resistor discharges the capacitor. It must drop the capacitor back to 0V, to fully reset the capacitor.
Of course you would replace the switches with transistors/ mosfets.
Suggestions for boosting 12V to 36V or higher:
* voltage tripler (or quadrupler) topology
* boost converter.