A study on the varieties of equivalent cordial labeling graphs

M. E. Abdel-Aal; S. A. Bashammakh; M. E. Abdel-Aal; S. A. Bashammakh

doi:10.3934/math.20241653

AIMS Mathematics

2024, Volume 9, Issue 12: 34720-34733. doi: 10.3934/math.20241653

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Research article

A study on the varieties of equivalent cordial labeling graphs

M. E. Abdel-Aal ^{1
,
,},
S. A. Bashammakh ²

1.
Department of Mathematics, Faculty of Science, Banha University, Banha 13518, Egypt
2.
Mathematics and Statistics Department, Faculty of Science, University of Jeddah, P. O. Box 80327, Jeddah 21589, Saudi Arabia

Received: 23 September 2024 Revised: 23 November 2024 Accepted: 03 December 2024 Published: 12 December 2024
MSC : 05C25, 05C75, 05C78

The concepts of cordial labeling, signed product cordiality, and logical cordiality have been introduced independently by different researchers as distinct labeling schemes. In this paper, we demonstrate the equivalence of these concepts. Specifically, we prove that a graph $ G $ is cordial if and only if it is signed product cordial, if and only if it is logically cordial. Additionally, we establish that a graph $ G $ admits permuted cordial labeling if and only if it exhibits cubic roots cordial labeling. Furthermore, we leverage this newfound equivalence to analyze the cordiality properties of several standard graphs.
- graph labeling,
- cordial graph,
- signed product cordial,
- logical cordial graph
Citation: M. E. Abdel-Aal, S. A. Bashammakh. A study on the varieties of equivalent cordial labeling graphs[J]. AIMS Mathematics, 2024, 9(12): 34720-34733. doi: 10.3934/math.20241653

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Abstract

The concepts of cordial labeling, signed product cordiality, and logical cordiality have been introduced independently by different researchers as distinct labeling schemes. In this paper, we demonstrate the equivalence of these concepts. Specifically, we prove that a graph $ G $ is cordial if and only if it is signed product cordial, if and only if it is logically cordial. Additionally, we establish that a graph $ G $ admits permuted cordial labeling if and only if it exhibits cubic roots cordial labeling. Furthermore, we leverage this newfound equivalence to analyze the cordiality properties of several standard graphs.

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