Affiliations: Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, India
Correspondence:
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Corresponding author. Sankar Sahoo, Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore 721102, India. E-mail: [email protected].
Abstract: In this paper, edge irregular intuitionistic fuzzy graphs, edge totally irregular intuitionistic fuzzy graphs, highly edge irregular intuitionistic fuzzy graphs and highly edge totally irregular intuitionistic fuzzy graphs are introduced. Some properties of an edge irregular intuitionistic fuzzy graphs and highly edge irregular intuitionistic fuzzy graphs are discussed. A equivalent condition under which edge irregular intuitionistic fuzzy graphs and edge totally irregular intuitionistic fuzzy graphs is provided. Also, we introduced a strong edge irregular intuitionistic fuzzy graphs, strong edge totally irregular intuitionistic fuzzy graphs, neighbourly edge irregular intuitionistic fuzzy graphs and neighbourly edge totally irregular intuitionistic fuzzy graphs with suitable illustrations and established many interesting results on them. Finally, edge irregularity and highly edge irregularity on some intuitionistic fuzzy graphs whose crisp graphs a path and a cycle are studied.
