Correct. Gandhi's assassin, Nathuram Godse, was a member of the Akhil Bharatiya Hindu Mahasabha.
It was founded as an anti-Christian, anti-Muslim political organization in 1915.
It's first vice president, Keshava Baliram Hedgewar, left the ABHM to form a fascist paramilitary organization - modeled on Mussolini's Blackshirts - called Rashtriya Swayamsevak Sangh.
The ABHM and the RSS had a working relationship for decades. The RSS began toning down the fascist pageantry in the 1950s and in 1952 elements from both groups formed the Bharatiya Jana Sangh, a Hindu nationalist political party, under the leadership of Shyama Prasad Mukherjee who had served as the head of ABHM in Bengal.
In 1980, Mukherjee's protege Atal Bihari Vajpayee formed a new Hindu nationalist party based from the BJS and other smaller and even more radical Hindutva (Hindu racial nationalist) organizations.
The new party was called the Bharatiya Janata.
Vajpayee became Prime Minster from 1998-2004.
So, basically, Gandhi's assassin's ideology triumphed over Gandhi's ideals at the Indian polls.