Hub Number in Ring Fuzzy Graphs and Restricted Hyper-Totient Fuzzy Graphs

Mohammed Alsharafi; Haifa Ahmed; Saad S. Al-Tobaili

Hub Number in Ring Fuzzy Graphs and Restricted Hyper-Totient Fuzzy Graphs

Abstract

In this paper, we introduce and study the hub number of ring fuzzy graphs. To make the construction self-contained, a ring fuzzy graph is treated as a weighted fuzzy structure RFΓ = (V, E, μ, σ) whose underlying vertices are ring-induced substructures and whose hub number is computed by the total vertex-membership value of a minimal hub set. We investigate this parameter for several important classes of ring fuzzy graphs, including complete, path, cycle, and star ring fuzzy graphs, and obtain explicit expressions in each case. In addition, we derive general bounds for the hub number in terms of the complement graph and several neighborhood-based parameters. Relationships between the hub number and other graph-theoretic quantities, such as domination-type and chromatic-type parameters, are also examined. Furthermore, we extend the study to restricted hyper-totient fuzzy graphs and present a characterization of their hub number. Finally, we analyze the behavior of the hub number under several operations on ring fuzzy graphs, including intersection, union, direct product, and direct sum, stating the required compatibility assumptions on the underlying vertex sets and membership functions. The results obtained in this work show that the hub number is a useful structural parameter for the analysis of ring fuzzy graphs and provide a foundation for further investigations in algebraic fuzzy graph theory.

Keywords

References

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Details

Primary Language

English

Subjects

Combinatorics and Discrete Mathematics (Excl. Physical Combinatorics)

Journal Section

Research Article

Authors

Mohammed Alsharafi ^*
0000-0001-6252-8968
Yemen

Haifa Ahmed This is me
0000-0002-4881-6493
Yemen

Saad S. Al-Tobaili
0009-0008-3225-3447
Yemen

Publication Date

June 30, 2026

Submission Date

April 10, 2026

Acceptance Date

June 2, 2026

Published in Issue

Year 2026 Volume: 3 Number: 3(1)

IZ

https://izlik.org/JA37DB53TN

Cite

RIS / Bibtex

APA

Alsharafi, M., Ahmed, H., & Al-Tobaili, S. S. (2026). Hub Number in Ring Fuzzy Graphs and Restricted Hyper-Totient Fuzzy Graphs. Türkiye Mathematical Sciences, 3(3(1), 55-75. https://izlik.org/JA37DB53TN

AMA

1.Alsharafi M, Ahmed H, Al-Tobaili SS. Hub Number in Ring Fuzzy Graphs and Restricted Hyper-Totient Fuzzy Graphs. TMS. 2026;3(3(1):55-75. https://izlik.org/JA37DB53TN

Chicago

Alsharafi, Mohammed, Haifa Ahmed, and Saad S. Al-Tobaili. 2026. “Hub Number in Ring Fuzzy Graphs and Restricted Hyper-Totient Fuzzy Graphs”. Türkiye Mathematical Sciences 3 (3(1): 55-75. https://izlik.org/JA37DB53TN.

EndNote

Alsharafi M, Ahmed H, Al-Tobaili SS (June 1, 2026) Hub Number in Ring Fuzzy Graphs and Restricted Hyper-Totient Fuzzy Graphs. Türkiye Mathematical Sciences 3 3(1) 55–75.

IEEE

[1]M. Alsharafi, H. Ahmed, and S. S. Al-Tobaili, “Hub Number in Ring Fuzzy Graphs and Restricted Hyper-Totient Fuzzy Graphs”, TMS, vol. 3, no. 3(1), pp. 55–75, June 2026, [Online]. Available: https://izlik.org/JA37DB53TN

ISNAD

Alsharafi, Mohammed - Ahmed, Haifa - Al-Tobaili, Saad S. “Hub Number in Ring Fuzzy Graphs and Restricted Hyper-Totient Fuzzy Graphs”. Türkiye Mathematical Sciences 3/3(1) (June 1, 2026): 55-75. https://izlik.org/JA37DB53TN.

JAMA

1.Alsharafi M, Ahmed H, Al-Tobaili SS. Hub Number in Ring Fuzzy Graphs and Restricted Hyper-Totient Fuzzy Graphs. TMS. 2026;3:55–75.

MLA

Alsharafi, Mohammed, et al. “Hub Number in Ring Fuzzy Graphs and Restricted Hyper-Totient Fuzzy Graphs”. Türkiye Mathematical Sciences, vol. 3, no. 3(1), June 2026, pp. 55-75, https://izlik.org/JA37DB53TN.

Vancouver

1.Mohammed Alsharafi, Haifa Ahmed, Saad S. Al-Tobaili. Hub Number in Ring Fuzzy Graphs and Restricted Hyper-Totient Fuzzy Graphs. TMS [Internet]. 2026 Jun. 1;3(3(1):55-7. Available from: https://izlik.org/JA37DB53TN