“…Historically, indices of Zagreb can be considered the first degreeـbased topological indices, which apply to many scientific, chemical, physical and economic, etc. [22][23][24][25] Various studies related to group or ring theory aspects of the 𝑍 modulo via graph theory, see that [3][4][5][6][7][8][9][10][11]21,26] and the references therein. In 2018, Alwardi A. et al studied the entire Zagreb indices of graphs [2].…”