Text this: Twin chromatic indices of some graphs with maximum degree 3

   _____   _    _    _    _    __   __   _    _   
  / ___// | || | || | |  | ||  \ \\/ // | || | || 
  \___ \\ | || | || | |/\| ||   \ ` //  | || | || 
  /    // | \\_/ || |  /\  ||    | ||   | \\_/ || 
 /____//   \____//  |_// \_||    |_||    \____//  
`-----`     `---`   `-`   `-`    `-`'     `---`