Abstract
The concept of domination is one of the most significant topics in graph theory to handle unpredictable phenomena. In this study, an unprecedented idea of domination is introduced in m-polar interval-valued fuzzy graph (m-PIVFG). Domination number (DN), isolated vertex, total dominating set, independent set of domination on m-PIVFG are discussed. Some algebraic properties of domination on m-PIVFG are investigated. Weak domination, strong domination, split and non-split domination, cototal and global dominating sets on m-PIVFG are investigated with some fundamental hypotheses and models. We explore the concept of domination in m-PIVFG by solving a case study of locating new facilities to handle a catastrophe reaction activity due to the "COVID-19 pandemic" in West Bengal, India. Ultimately, conclusions and avenues of future scopes are placed at the end of this study.