Matching Concepts of m-Polar Fuzzy Incidence Graphs

Mitu, Dilara Akter; Yang, Weihua; Ali, Abid; Mahapatra, Tanmoy; Ali, Gohar; Popa, Ioan-Lucian

doi:10.3390/sym17071160

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Matching Concepts of m-Polar Fuzzy Incidence Graphs

by

Dilara Akter Mitu

¹

,

Weihua Yang

^1,*,

Abid Ali

¹,

Tanmoy Mahapatra

²

,

Gohar Ali

³

and

Ioan-Lucian Popa

^4,5,*

¹

College of Mathematics, Taiyuan University of Technology, Wanbailin District, Taiyuan 030024, China

²

Department of Mathematics, Ramkrishna Mahato Govt. Engg. College, Purulia 723103, India

³

Department of Mathematics, Islamia College Peshawar, Peshawar 25120, Khyber Pakhtunkhwa, Pakistan

⁴

Department of Computing, Mathematics and Electronics, 1 Decembrie 1918 University of Alba Iulia, 510009 Alba Iulia, Romania

⁵

Faculty of Mathematics and Computer Science, Transilvania University of Brasov, Iuliu Maniu Street 50, 500091 Brasov, Romania

^*

Authors to whom correspondence should be addressed.

Symmetry 2025, 17(7), 1160; https://doi.org/10.3390/sym17071160

Submission received: 11 June 2025 / Revised: 7 July 2025 / Accepted: 18 July 2025 / Published: 20 July 2025

(This article belongs to the Special Issue Symmetry and Graph Theory, 2nd Edition)

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Abstract

The m-Polar Fuzzy Incidence Graph (m-PFIG) is an extension of the m-Polar Fuzzy Graph (m-PFG), which provides information on how vertices affect edges. This study explores the concept of matching within both bipartite and general m-polar fuzzy incidence graphs (m-PFIGs). It extends various results and theorems from fuzzy graph theory to the framework of m-PFIGs. This research investigates various operations within m-PFIGs, including augmenting paths, matching principal numbers, and the relationships among them. It focuses on identifying the most suitable employees for specific roles and achieving optimal outcomes, particularly in situations involving internal conflicts within an organization. To address fuzzy maximization problems involving vertex–incidence pairs, this study outlines key properties of maximum matching principal numbers in m-PFIGs. Ultimately, the matching concept is applied to attain these maximum principal values, demonstrating its effectiveness, particularly in bipartite m-PFIG scenarios.

Keywords: m-polar fuzzy graph; m-polar fuzzy incidence graph; matching; maximum matching

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MDPI and ACS Style

Mitu, D.A.; Yang, W.; Ali, A.; Mahapatra, T.; Ali, G.; Popa, I.-L. Matching Concepts of m-Polar Fuzzy Incidence Graphs. Symmetry 2025, 17, 1160. https://doi.org/10.3390/sym17071160

AMA Style

Mitu DA, Yang W, Ali A, Mahapatra T, Ali G, Popa I-L. Matching Concepts of m-Polar Fuzzy Incidence Graphs. Symmetry. 2025; 17(7):1160. https://doi.org/10.3390/sym17071160

Chicago/Turabian Style

Mitu, Dilara Akter, Weihua Yang, Abid Ali, Tanmoy Mahapatra, Gohar Ali, and Ioan-Lucian Popa. 2025. "Matching Concepts of m-Polar Fuzzy Incidence Graphs" Symmetry 17, no. 7: 1160. https://doi.org/10.3390/sym17071160

APA Style

Mitu, D. A., Yang, W., Ali, A., Mahapatra, T., Ali, G., & Popa, I.-L. (2025). Matching Concepts of m-Polar Fuzzy Incidence Graphs. Symmetry, 17(7), 1160. https://doi.org/10.3390/sym17071160

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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