power of BOD to fill up vacancy caused by resignation of dir

Yes, Sec 262 empowers the BOD to fill casual vacancy (created on account of death, insanity, insolvency or resignation of a Director) in the case of a Public company or a private company being subsidiary of a Public company. Resignation is not a case outside the purview of casual vacancy. So casual vacancy created on account of resignation of a Director is covered under the powers expressed in Sec 262 as mentioned above.