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 \(\bar{G}\) of G. In this paper, an innovative concept of \(\alpha\) - Cut diminish fuzzy graph G\(^\alpha\) (\(\sigma^\alpha,\mu^\alpha\)) and \(\alpha\) - Cut strong arc of \(\alpha\)- Cut diminish Fuzzy graph are introduced in the new domain. Further complements of \(\alpha\) - Cut diminish fuzzy graph are discussed with a new approach. Definition of \(\alpha\)- Cut strong domination and Global Strong domination in \(\alpha\)- Cut diminish fuzzy graph are also introduced by \(\alpha\)- Cut strong arc. Moreover, some standard theorems and related results in Global domination of \(\alpha\)- Cut diminish fuzzy graph are presented with suitable examples of Standard \(\alpha\) - Cut diminish fuzzy graph.
Author
(s) Details
V.
Senthilkumar
Department of Mathematics, CPA College, Bodinayakanur, India.
Please see the book here:- https://doi.org/10.9734/bpi/mcscd/v7/2781
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