Siyamak Firouzian - Department of Mathematics, Payame Noor University (PNU), Tehran, Iran
Shaban Sedghi - Department of Mathematics‎, ‎Qaemshahr Branch‎, ‎Islamic Azad University‎, ‎Qaemshahr‎, ‎Iran
Nabi Shobe - Department of Mathematics‎, ‎Babol Branch‎, ‎Islamic Azad University‎, ‎Babol‎, ‎Iran

In this paper‎, ‎we introduce some new concepts of fuzzy graphs with the notion of degree of an edge in fuzzy line graphs and congraphs‎. ‎Also‎, ‎some properties and some‎ ‎lemmas of edge fuzzy line graphs and congraphs are studied‎. ‎Finally‎, ‎we state and prove some results‎ ‎related to these concepts.

Fuzzy graph‎, ‎Fuzzy line graph‎, ‎Fully connected graph‎, ‎Common neighborhood graph‎, ‎Congraph