The hero of the 1965 India-Pakistan war and the only Air Force officer to be promoted to five-star rank, Singh died in Delhi yesterday. He was 98.
The governor said the officer's outstanding leadership in the 1965 war would always be remembered.
"In the death of Air Marshal Arjan Singh, the nation had lost a highly decorated soldier, who was always ready to defend the borders," he said in his condolence message.
There would be no official celebrations and the national flag would fly at half-mast at all government buildings in Punjab during these three days, an official spokesperson said earlier.
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Former chief minister Parkash Singh Badal also condoled the passing away of Singh.
Badal, in a meeting this morning, also asked Shiromani Gurdwara Parbandhak Committee chief Kirpal Singh Badungar to place a picture of Singh in the Sikh museum in Amritsar.
A state funeral will be accorded to Singh and his last rites would be performed at Delhi tomorrow.