Global Domination of \(α\)- Cut Diminish Fuzzy Graph - V. Senthilkumar (Mathematics and Computer Science: Contemporary Developments Vol. 7, 2024)
Fuzzy graph is the generalization of the ordinary graph. A dominating set D of a graph G, is a global dominating set in G if D is also a dominating set of \(G\) of G. In this paper, an innovative concept of \(α\) - Cut diminish fuzzy graph G\(^α\) (\(σ^α,μ^α\)) and \(α\) - Cut strong arc of \(α\)- Cut diminish Fuzzy graph are introduced in the new domain. Further complements of \(α\) - Cut diminish fuzzy graph are discussed with a new approach. Definition of \(α\)- Cut strong domination and Global Strong domination in \(α\)- Cut diminish fuzzy graph are also introduced by \(α\)- Cut strong arc. Moreover, some standard theorems and related results in Global domination of \(α\)- Cut diminish fuzzy graph are presented with suitable examples of Standard \(α\) - Cut diminish fuzzy graph.