• P-ISSN 0974-6846 E-ISSN 0974-5645

# Indian Journal of Science and Technology

## Article

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Indian Journal of Science and Technology

Year: 2023, Volume: 16, Issue: Special Issue 4, Pages: 8-17

Original Article

## Subdivision of Eccentric Fuzzy Graphs

Received Date:12 October 2023, Accepted Date:22 November 2023, Published Date:25 December 2023

## Abstract

Objectives: To present a recursion formula on the order of an eccentric fuzzy graph and the same is found by subdividing the set of lines in it. Methods: Here, a special fuzzy graph known as an eccentric fuzzy graph denoted by EF(G): , which is derived by eccentricity and diameter of a crisp graph :(P,L) with membership function of point set and line set is considered. In this article, the wheel and ladder graph were mainly discussed. Findings: With membership function of Eccentric fuzzy graph, the order of an eccentric fuzzy ladder graph was established and the same is found by subdividing the lines on the left path, right path and on both. Further, order for an eccentric fuzzy wheel graph by subdividing rim, spoke and both. Additionally, recursion formulas for atop were found. Novelty: This is the first article which deals with the order of an eccentric fuzzy graph by subdividing edges. 2020 A.M.S Mathematical Subject Classification: 03E72, 05C07, 05C12, 05C69.

Keywords: Fuzzy sets, Fuzzy Graph, Distance in graph, Vertex degree, subdivision

## References

1. Meenal N. A First Look at Eccentric Fuzzy Graphs. International Journal of Research and Analytical Reviews (IJRAR). 2019;6(1):188–194. Available from: https://ijrar.org/papers/IJRAR19J1029.pdf
2. Meenal N, Jovita JJ. On Regular Inverse Eccentric Fuzzy Graph. Applications and Applied Mathematics. 2022;17(3):119–128. Available from: https://digitalcommons.pvamu.edu/aam/vol17/iss3/10/
3. Meenal N, Jovita JJ. A first look at inverse eccentric fuzzy graph. In: INTERNATIONAL CONFERENCE ON RECENT ADVANCES IN MATHEMATICS AND COMPUTATIONAL ENGINEERING: ICRAMCE 2022, AIP Conference Proceedings. Chennai, India, 6–7 January 2022. AIP Publishing. 2829, Issue 1.