Carrying on (allegedly) with "different men from the neighborhood": haram. Murdering with an axe the person so accused: halal.

It is no accident or coincidence that Muslims commit 91 percent of honor killings worldwide. A manual of Islamic law certified as a reliable guide to Sunni orthodoxy by Al-Azhar University, the most respected authority in Sunni Islam, says that "retaliation is obligatory against anyone who kills a human being purely intentionally and without right." However, "not subject to retaliation" is "a father or mother (or their fathers or mothers) for killing their offspring, or offspring's offspring." ('Umdat al-Salik o1.1-2). In other words, someone who kills his child incurs no legal penalty under Islamic law.

Syria in 2009 scrapped a law limiting the length of sentences for honor killings, but "the new law says a man can still benefit from extenuating circumstances in crimes of passion or honour 'provided he serves a prison term of no less than two years in the case of killing.'" And in 2003 the Jordanian Parliament voted down on Islamic grounds a provision designed to stiffen penalties for honor killings. Al-Jazeera reported that "Islamists and conservatives said the laws violated religious traditions and would destroy families and values."

Nonetheless, the media... http://www.jihadwatch.org/2012/01/pakistan-muslim-murders-sister-with-ax...