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Interval-Valued Fuzzy Graphs
International Journal of Fuzzy Logic and Intelligent Systems 2020;20(4):316-323
Published online December 25, 2020
© 2020 Korean Institute of Intelligent Systems.

Tarasankar Pramanik1, Sovan Samanta2, and Madhumangal Pal3

1Department of Mathematics, Khanpur Gangche High School, Midnapore, 721201, India
2Department of Mathematics, Tamralipta Mahavidyalaya, Tamluk, India
3Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, India
Correspondence to: Sovan Samanta (
Received February 26, 2020; Revised December 10, 2020; Accepted December 11, 2020.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Interval-valued fuzzy graphs (IVFGs) are a generalization of fuzzy graphs. In this article, the sum distance between vertices in an IVFG is introduced. This definition satisfies the metric properties. In addition, some important aspects related to eccentricity, radius, and diameter are proved. The necessary and sufficient conditions for a vertex to be eccentric are established. The relationship between eccentricities and the sum distance between two vertices is derived. An algorithm is presented to determine the sum distance between two vertices in interval-valued fuzzy graphs. Furthermore, some related theorems for the complete IVFG are deduced.
Keywords : Sum distance, Eccentricity, Interval-valued fuzzy graphs