Strangers on a Train (1950) by Patricia Highsmith
The psychologists would call it folie a deux...
"Bruno slammed his palms together. 'Hey! Cheeses, what an idea! I kill your wife and you kill my father! We meet on a train, see, and nobody knows we know each other! Perfect alibis! Catch?'"
From this moment, almost against his conscious will, Guy Haines is trapped in a nightmare of shared guilt and an insidious merging of personalities.