Is it mandatory?

No.  It is not mandatory.  But you have to register the death of the deceased at the Municipal Corporation/Municipality or Panchayat and get the death certificate for further necessities like pension, legal heir certificate etc.

It is not mandatory to publish the death of a person in a local newspaper.

In general newspaper publication is given only to inform public and relatives about the death so that the information is conveyed.

It is compulsory to get it registered with local authority and need not publish as advised by senior experts, which I fully agree and appreciate.