Dear Roshni,
Logically, the "notice period" will start from the next date of resignation (be it a weekend or holiday).
As rightly said by Mr. Madhu T.K., the notice period is given to choose an alternative option (from each side). So if an employee resigns on Friday, then the period (for alternative) will start from Saturday. Therefore, the weekend should be counted as part of the notice period. However, in respect of Mr. Madhu's advice related to "An HR person should be practical in dealing with such situations," I would like to add that in some cases, HRs have to be answerable for how they dealt with the situation and what company policy and contract terms apply to the situation. Hence, for them, it is difficult to deal practically and more important to keep themselves in a safe position.
Dear P-Lekha Jacobs,
I observed your suggestions are described in a proper way: 1. Description of the query, 2. Advice, and 3. Utmost advice. That gives clear and wide ideas to the poster on how to deal with the scenarios.
In this case, there may be no resignation or termination policies in the establishment. Hence, the query raised by the poster.