Original Research Article

Article volume = 2023 and issue = 2

Pages: 110–119

Article publication Date: November 22, 2023

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# An Analysis of Hub Number in Various Fuzzy Graphs

#### Saad Tobaili(a), Haifa Ahmed(b), and Mohammed Alsharafi(c)

(a) Department of Mathematics, Faculty of Science, Hadhramout University, Mukalla, Yemen.

(b) Department of Mathematics, Faculty of Education, Art and Science, Aden University, Aden, Yemen

(C) Department of Mathematics, Faculty of Arts and Science, Yildiz Technical University, Istanbul, Turkey.

##### Abstract:

In the present work, we aim to talk about the analytical findings about the quantification of hub structures arising from various graph operations applied to pairwise combinations of connected graphs and paths. Specifically, we delineate the hub numbers resulting from the intersection and joining of two interconnected graphs. We also derive the hub numbers for the intersection of two complete fuzzy graphs, as well as the intersection of a non-exhaustive connected fuzzy graph and complete fuzzy graphs. Moreover, we determine the hub configuration for the intersection of two paths, denoted Pn and Pm, whereby n ⩾ 2 and m ⩾ 3. In addition to enumerating these hub values, we provide an upper boundary on the maximum hub number attainable by taking the join of two paths Pn and Pm, where 2 ⩽ m ⩽ n. Through a rigorous mathematical treatment of these graph constructions and evaluations of their associated hub structures, the present work aims to systematically characterize and compare the topological properties induced by different relational combinations of graphs and paths. It is hoped that the communication of these findings will provide novel insight into the structural transformations and complexity changes incurred by various graph operations.

##### Keywords:

Hub number; fuzzy graph operations; complete fuzzy graph

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##### Cite this article as:

- Saad Tobaili, Haifa Ahmed, and Mohammed Alsharafi, An Analysis of Hub Number in Various Fuzzy Graphs, Communications in Combinatorics, Cryptography & Computer Science, 2023(2), PP.110–119, 2023
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