A single assignment of numbers for square divisor cordial and cube divisor cordial labelings on the generalized Petersen graphs GP (n,3)

Fredrick Ignatius () and S. Kaspar
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Fredrick Ignatius: Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014 Tamil Nadu, India
S. Kaspar: Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014 Tamil Nadu, India

International Journal of Modern Physics C (IJMPC), 2025, vol. 36, issue 08, 1-18

Abstract: In this paper, a work on the generalized Petersen graph GP (n,3) is done, proving Generalized Petersen graph GP (n,3) to be both Square Divisor Cordial Graphs and Cube Divisor Cordial Graphs by a single assignment of numbers on the same graph. Few conditions are provided to label the graphs in single assignment to prove two different labelings. A rule is developed to label the graphs and the results obtained are tabulated by actual verification for n=4 to n=30 but the rule holds good for all n≥ 4. Further, a few illustrations are provided to justify the rule given to label the graphs in a single assignment.

Keywords: Generalized Petersen graphs; square divisor cordial labeling and cube divisor cordial labeling (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0129183124410018

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