In this paper we introduce the concept of edge domination and total edge domination in intuitionistic fuzzy graphs. We determine the edge domination number and total edge domination number for several classes of intuitionistic fuzzy graphs and obtain bounds for them. We also obtain Nordhaus gaddum type results for the parameters.

A graph G is domination dot-critical, or just dot-critical, if contracting any edge decreases the domination number. It is totally dot-critical if identifying any twovertices decreases the domination number. In this paper, we study an open question concerning of the diameter of a domination dot-critical graph G. © 2008 Elsevier B.V. All rights reserved.