You should not re-marry.
Luke 16:18: Everyone who divorces his wife and marries another commits adultery, and he who marries a woman divorced from her husband commits adultery.
Mark 10:11-12: And he said to them, 'Whoever divorces his wife and marries another commits adultery against her; 12 and if she divorces her husband and marries another, she commits adultery.'
1 Corinthians 7:10–11 (ESV)
10 To the married I give this charge (not I, but the Lord): the wife should not separate from her husband 11 (but if she does, she should remain unmarried or else be reconciled to her husband), and the husband should not divorce his wife.
A second marriage is permissible only if the first spouse dies.
1 Corinthians 7:39 (ESV)
39 A wife is bound to her husband as long as he lives. But if her husband dies, she is free to be married to whom she wishes, only in the Lord.
Romans 7:1-3, Do you not know, brethren—for I am speaking to those who know the law—that the law is binding on a person only during his life? 2 Thus a married woman is bound by law to her husband as long as he lives; but if her husband dies she is discharged from the law concerning her husband. 3 Accordingly, she will be called an adulteress if she lives with another man while her husband is alive. But if her husband dies she is free from that law, if she marries another man she is not an adulteress.
That is to say; Couple A married for first time, spouse dies in car accident at 35, other spouse is free to marry. <-- no divorce in this situation