Metricity of super-knight's distance in digital geometry

Abstract In this paper we have extended the knight's moves in chess to introduce super-knight's moves in digital geometry. They define super-knight's distance (like the knight's distance [1]). However, all super-knight's distances are not metrics. We have proved a theorem to show that a super-knight's distance is a metric if and only if the underlying super-knight's move is well-behaved in a specific sense. We conclude with suggestions on future study.