Abstract: We solved the problems of the optimal vertex-distinguishing Ⅰ-total colorings (VDITC) and the optimal vertex-distinguishing Ⅵ-total colorings (VDVITC) of graph mC₁₅ by constructing a matrix with color sets and empty set as its elements, and using the methods of distributing color sets in advance and describing coloring explicitly, and obtained vertex-distinguishing Ⅰ-total chromatic numbers and the vertex-distinguishing Ⅵ-total chromatic numbers of graph mC₁₅. The results  show that the VDITC conjecture and VDVITC conjecture are valid for graph mC₁₅.

Key words: vertex-distinguishing Ⅰ-total colorings, vertex-distinguishing Ⅵ-total colorings, vertex-distinguishing Ⅰ-total chromatic numbers, vertex-distinguishing Ⅵ-total chromatic numbers