A novel concept of domination in m-polar interval-valued fuzzy graph and its application

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.

A Novel Approach on Energy of λJ-dominating Single-Valued Neutrosophic Graph Structure

“…The following studies [23][24][25] provide some helpful information about these kinds of structures. In 2022, Bera, S., and Pal, M. [26] presented a new idea regarding domination in m-polar interval-valued FG. The idea of edge-vertex domination on interval graphs in 2024 was recently introduced by Shambayati, H., Shafiei Nikabadi, M., Saberi, S., et al [27].…”