Document Type : Research Paper

Author

GOVT ARTS AND SCIENCE COLLEGE, KONDOTTY

10.22105/jfea.2022.354342.1227

Abstract

Sambathkumar introduces the notion of global domination in graphs. According to him, a dominating set S of G is a global dominating set of G if S is also a dominating set of the complement of G.

Nagoorgani and Jahir Hussain introduced the concept of global domination in

fuzzy graphs using effective arcs. This paper presents global domination in

fuzzy graphs using strong arcs. The strong global domination number of different classes of fuzzy graphs is obtained. An upper bound for the strong global

domination number of fuzzy graphs is obtained. Strong global domination in

fuzzy trees is studied. It is established that every node of a strong global dominating set of a fuzzy tree is either a fuzzy cut node or a fuzzy end node. It

is proved that in a fuzzy tree each node of a strong global dominating set is

incident on a fuzzy bridge. Also, the characteristic properties of the existence

of a strong global dominating set for a fuzzy graph and its complement are

established

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Main Subjects