murder

noun
1.
Law . the killing of another human being under conditions specifically covered in law. In the U.S., special statutory definitions include murder committed with malice aforethought, characterized by deliberation or premeditation or occurring during the commission of another serious crime, as robbery or arson (first-degree murder), and murder by intent but without deliberation or premeditation (second-degree murder).

There you go, argument settled. It is not murder unless the law says it is. State sanctioned execution is not murder. I am not saying that it is moral or right. But it is not murder.