$\rho$-Level Sets of a NS and Its Infinite Extendable Graphs

Rakhal Das; Debjani Rakshit

doi:10.32323/ujma.1669933

$\rho$-Level Sets of a NS and Its Infinite Extendable Graphs

Abstract

Johnson Awolola defined the $\alpha$-level neutrosophic set in the year 2020. However, this definition is not useful for getting some realistic results. In order to generate more realistic and applicable results, we have introduced a new concept of the $\rho$-level NSs in the form of $\rho$-lower level and $\rho$-upper level sets of a NS. Using several real-world examples, such as choosing personnel for an institutional objective, we discussed our outcomes. Using these examples, we also illustrate the significance of the $\rho$-level NS's, upper and lower boundaries. Along with studying numerous features, we also applied these results to the NG and defined various classes of infinite extendable NGs. Additionally, the theoretical frameworks for infinitely extensible NGs have been developed, with different supporting examples.

Keywords

Infinitely extendable graph , Neutrosophic graph(NG) , Neutrosophic set(NS) , $\rho$-Lower level set , $\rho$-Upper level set

References

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Details

Primary Language

English

Subjects

Algebra and Number Theory

Journal Section

Research Article

Authors

Rakhal Das
0000-0002-0895-2976
India

Debjani Rakshit ^*
0000-0001-8877-6484
India

Early Pub Date

December 8, 2025

Publication Date

December 11, 2025

Submission Date

April 4, 2025

Acceptance Date

November 27, 2025

Published in Issue

Year 2025 Volume: 8 Number: 4

DOI

https://doi.org/10.32323/ujma.1669933

IZ

https://izlik.org/JA99MR53XW

APA

Das, R., & Rakshit, D. (2025). $\rho$-Level Sets of a NS and Its Infinite Extendable Graphs. Universal Journal of Mathematics and Applications, 8(4), 211-218. https://doi.org/10.32323/ujma.1669933

AMA

1.Das R, Rakshit D. $\rho$-Level Sets of a NS and Its Infinite Extendable Graphs. Univ. J. Math. Appl. 2025;8(4):211-218. doi:10.32323/ujma.1669933

Chicago

Das, Rakhal, and Debjani Rakshit. 2025. “$\rho$-Level Sets of a NS and Its Infinite Extendable Graphs”. Universal Journal of Mathematics and Applications 8 (4): 211-18. https://doi.org/10.32323/ujma.1669933.

EndNote

Das R, Rakshit D (December 1, 2025) $\rho$-Level Sets of a NS and Its Infinite Extendable Graphs. Universal Journal of Mathematics and Applications 8 4 211–218.

IEEE

[1]R. Das and D. Rakshit, “$\rho$-Level Sets of a NS and Its Infinite Extendable Graphs”, Univ. J. Math. Appl., vol. 8, no. 4, pp. 211–218, Dec. 2025, doi: 10.32323/ujma.1669933.

ISNAD

Das, Rakhal - Rakshit, Debjani. “$\rho$-Level Sets of a NS and Its Infinite Extendable Graphs”. Universal Journal of Mathematics and Applications 8/4 (December 1, 2025): 211-218. https://doi.org/10.32323/ujma.1669933.

JAMA

1.Das R, Rakshit D. $\rho$-Level Sets of a NS and Its Infinite Extendable Graphs. Univ. J. Math. Appl. 2025;8:211–218.

MLA

Das, Rakhal, and Debjani Rakshit. “$\rho$-Level Sets of a NS and Its Infinite Extendable Graphs”. Universal Journal of Mathematics and Applications, vol. 8, no. 4, Dec. 2025, pp. 211-8, doi:10.32323/ujma.1669933.

Vancouver

1.Rakhal Das, Debjani Rakshit. $\rho$-Level Sets of a NS and Its Infinite Extendable Graphs. Univ. J. Math. Appl. 2025 Dec. 1;8(4):211-8. doi:10.32323/ujma.1669933