The board may refuse to issue a license by examination to a dental or dental hygiene applicant if the person:

(1) presents to the board fraudulent or false evidence of the person's qualification for examination or license;
(2) is guilty of any illegality, fraud, or deception during the examination or the process to secure a license;
(3) is habitually intoxicated or is addicted to drugs;
(4) commits a dishonest or illegal practice in or connected to dentistry or dental hygiene;
(5) is convicted of a felony under a federal law or law of this state; or
(6) is found to have violated a law of this state relating to the practice of dentistry within the 12 months preceding the date the person filed an application for a license to practice dentistry or dental hygiene.

http://www.statutes.legis.state.tx.us/Docs/OC/htm/OC.263.htm#263.001

(a) The board, after notice and hearing, may reprimand a person who holds a license issued under this subtitle, issue a warning letter to a person licensed under this subtitle, impose a fine on a person licensed under this subtitle, impose an administrative penalty under Subchapter A, Chapter 264, on a person who holds a license under this subtitle, place on probation with conditions a person whose license has been suspended, or revoke or suspend a person's license issued under this subtitle if the person:

(1) is adjudged under the law to be insane;
(2) is convicted of a misdemeanor involving fraud or a felony under federal law or the law of any state;

http://www.statutes.legis.state.tx.us/Docs/OC/htm/OC.263.htm#263.002

(a) The board shall suspend a license holder's license issued under this subtitle on proof that the person has been:

(1) initially convicted of:

(A) a felony;

http://www.statutes.legis.state.tx.us/Docs/OC/htm/OC.263.htm#263.006