Distance Closed G-Eccentric Domination in Fuzzy Graphs

Abstract

A dominating set  of the vertex set  in a fuzzy graph  is said to be a g-eccentric dominating set if for every  at least one g-eccentric vertex  in . A subset  of a fuzzy graph  is said to be distance closed set if for every vertex  and for every vertex  at least one vertex  such that . A subset  of a vertex set  in a fuzzy graph  is said to be distance closed g-eccentric dominating set if  is distance closed and  is g-eccentric dominating set. The lowest cardinality of the distance closed g-eccentric dominating set is called the distance closed g-eccentric domination number of . This article discusses the distance closed g-eccentric dominating set and its number in fuzzy graphs. Bounds for the distance closed g-eccentric domination number are found for several fuzzy graph types. Several theorems, results, and observations are presented on distance closed g-eccentric dominating sets and numbers in fuzzy graph