Abstract: In this paper, we present two new ranking and unranking
algorithms for k-ary trees represented by x-sequences in Gray
code order. These algorithms are based on a gray code generation algorithm
developed by Ahrabian et al.. In mentioned paper, a recursive
backtracking generation algorithm for x-sequences corresponding to
k-ary trees in Gray code was presented. This generation algorithm
is based on Vajnovszki-s algorithm for generating binary trees in
Gray code ordering. Up to our knowledge no ranking and unranking
algorithms were given for x-sequences in this ordering. we present
ranking and unranking algorithms with O(kn2) time complexity for
x-sequences in this Gray code ordering