Abstract

Regular and Edge Regular Interval Valued Fuzzy Graphs

Souriar Sebastian1 and Ann Mary Philip2

1Department of Mathematics, St. Alberts 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.

Keywords :Interval valued fuzzy graph, Degree, Total degree, Edge degree, Total edge degree, Regular IVFG, Totally regular IVFG, Partially regular IVFG, Fully regular IVFG, Edge regular IVFG, Totally edge regular IVFG, Partially edge regular IVFG, Fully edge regular IVFG.

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