Total Efficient Domination in Fuzzy Graphs

This study proposed total efficient domination in fuzzy graphs. The exact values on the total efficient domination number for several classes of fuzzy graphs are determined. A lower bound and an upper bound for the total efficient domination number in terms of maximum strong arc neighborhood degree and the order are obtained. In addition, a new relationship between total efficient domination number and total efficient domatic number is established. Finally, we design an algorithm to determine the minimum fuzzy cardinality of the total efficient dominating set of a fuzzy tree
$T$
or decide that
$T$
has no total efficient dominating set.