Regular and Edge Regular Interval Valued Fuzzy Graphs
Souriar Sebastian1 and Ann Mary Philip2
1Department of Mathematics,
St. Albert’s College, Kochi – 682018, Kerala, INDIA.
2Department of Mathematics,
Assumption College, Changanassery – 686101, Kerala, INDIA.
ABSTRACT
In this paper, we study about regular, totally regular, edge regular and totally edge regular interval valued fuzzy graphs (IVFGs). We prove some theorems related to degree and total degree of vertices and edges of IVFGs. We expose some properties of regular interval valued fuzzy graphs (RIVFGs) and totally regular interval valued fuzzy graphs (TRIVFGs) through various examples. Also, we compare edge regular interval valued fuzzy graphs (ERIVFGs) and totally edge regular interval valued fuzzy graphs (TERIVFGs) and we derive a necessary and sufficient condition under which they are equivalent. We also prove some other theorems which reveal the relationship between these concepts.