Title On the outer independent total double Roman dominating functions Type of Research Article Keywords On the outer independent total double Roman dominating functions Abstract On the outer independent total double Roman dominating functions Researchers Hossein Abdollahzadeh Ahangar (First Researcher)، Mustapha Chellali (Second Researcher)، Seyed Mahmoud Sheikholeslami Kavkani (Third Researcher)، Valenzuela-Tripodoro Valenzuela-Tripodoro (Fourth Researcher)