<b>Strong Regular L Fuzzy Graphs</b> In this paper, the notion of regular and strong regular L fuzzy graph is introduced. The conditions for strong regularity of L fuzzy graphs on cycle and star graph are derived. L fuzzy graph, strong L fuzzy graph, regular L fuzzy graph, strong regular L fuzzy graph 503-509 Issue-5 Volume-1 R. Seethalakshmi | R.B. Gnanajothi