MEXICO CITY, Oct 6 (Reuters) - The mayor of the capital of Mexico's violence-plagued state of Guerrero was killed on Sunday less than a week after he took office, the state's governor confirmed. Alejandro Arcos was killed just six days after he took office as mayor of the city of Chilpancingo, a city of around 280,000 people in southwestern Mexico. "His loss mourns the entire Guerrero society and fills us with indignation," Guerrero Governor Evelyn Salgado said in a statement shared on social...