Global Domination of \(\alpha\)- Cut Diminish Fuzzy Graph
DOI:
https://doi.org/10.9734/bpi/mcscd/v7/2781Keywords:
\(\alpha\)- Cut diminsh fuzzy graph, \(\alpha\) -Cut strong arc, \(\alpha\) - Cut non strong arc, complement of\(\alpha\)- Cut, \(\alpha\)-Cut Strong arc domination, \(\alpha\)- Cut strong global dominationAbstract
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.
