The day after Yom Tov is called Isru Chag.
One may not fast on Isru Chag and no Tachanun is said on Isru Chag.
Some do not say Tachanun for the entire week after Shavu'ot since the Korbanot you had to bring when coming to the Bet Hamikdash on Yom Tov could be brought for the entire week after Shavu'ot.
Source: Kitzur Shulchan Aruch 22:8, 103:14
- Danny Sunday, 8 Sivan 5769
Please daven for a complete recovery for Tamar bat Naama - תמר בת נעמה