Document Type : Research Paper
Author
Department of Mathematics, Govt Arts and Science College, Kondotty, Malappuram-673641, India.
Abstract
Sampathkumar [7] has been introduced the notion of global domination in graphs. Nagoorgani and Hussain [24] have 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.
Keywords
Main Subjects
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