The Henderson Police Department said in a Facebook post that Wendell Melton was arrested at the scene on felony charges of open murder, child abuse and firearms possession and "booked into the Henderson Detention Center."
Sonja Jones, the teen's former foster mother, told KSNV the boy was "abused physically and mentally and spiritually for many, many years" and said she believes he was killed because of his sexual orientation.
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"He hated the fact that his son was gay," Jones said of Melton. "I'm sure that inside of his mind, he would rather have a dead son than a gay son."
Jones added that it was her understanding that Melton had caught Giovanni "with his boyfriend before and pulled out a gun on him."
The Henderson Police Department declined to provide additional information regarding the circumstances surrounding the shooting due to it being "an active investigation." It was not clear whether Wendell Melton had obtained a defense lawyer, The Associated Press said.
Jaime Grant, executive director of PFLAG National, an LGBTQ family and ally organization, said Giovanni's death is part of broader societal issue.
"We have a crisis of masculinity in this country — it's obvious across the board in this report and in the unrelenting reports on sexual assault and also gun violence," Grant said in a statement provided to NBC News. "Many 'normative' messages men learn as they are growing up about stuffing their feelings, policing other men's gender and sexuality, asserting 'dominance' from the board room to the bedroom, also show up in their lives as fathers."